Magdalena:  I am not sure if I fully understand your question.  I live and work in the US.  I live in Florida, which was the first right-to-work state. My employer is unionized.

In 1935, the National Labor Relations Act created the National Labor Relations Board (NLRB).  The NLRB had two major tasks.  It would conduct union representation elections to see if a union did or did not have majority support. If a union prevailed, it had the duty to fairly represent all of the employees (i.e. not just its supporters). The second task involved five general categories of unfair labor practices (ULPs).  The NLRB would investigate ULP charges.  The NLRB would hold a hearing and make a decision.  These NLRB decisions were enforceable in federal court.  

Are you aware of what the "right-to-work" refers to?  This term was introduced in 1947 in the Labor Management Relations Act.  We currently have two different types of states.  Non-right-to-work states have union security provisions.  In simple terms, unions can collect regular dues and initiation fees from a new employee after a fixed period of time (30 days).  In right-to-work states, union dues paying is voluntary, and one can choose to join and pay dues or drop out at any time.  This could result in dues being paid by over 90% of the employees in non-right-to-work states and perhaps only 20-30% paying dues in right-to-work states.  In the second situation, a union is present, but is has few funds to support negotiation efforts, strikes, grievance processing, newsletters, surveys, etc.  Those who favor union security provisions argue unions are an industrial form of government.  Once the union prevails in an election, it has the right to collect dues for the services it must legally supply for all of the employees.  The dues are seen as being much like taxes paid to a government entity.  Dues paying members got to originally vote on whether there would be a union, and after this they get to periodically vote on union officers, and on the proposed collective bargaining agreements.  If people are allowed to get the representation, but not pay for it, they would be "free riders."  Right-to-work advocates argue if it is a good union, people will join and pay the dues.  Those who did not vote for the union, or feel it is not doing a good job should not be forced to pay dues.  Historically, the right-to-work states were lower wage states.  In order to attract investment and create new jobs, costs must be kept low.  Those providing the political funds to advocate for "individual freedom" have tended to be employers who wanted a "better business climate" in a state. 

Additionally, one could get into what union dues can be used for.  Conducting contract negotiations, grievance investigation and processing, conducting business meetings, union publications, litigation expenses, and the like are considered "chargeable expenditures."  "Nonchargeable activities" include the cost of legislative lobbying, union benefits not available to to financial core members and charitable contributions. 

 In many union organizing elections, some common campaign issues are raised. The union organizers will argue they will get the workers better wages, hours and working conditions.  They will stress seniority in assigning overtime and bidding on jobs.  A grievance procedure will be provided where a union steward will assist a grievant in enforcing the provisions of the union contract.  The final step of the grievance procedure, if a settlement has not been reached, is final and binding arbitration by a third party arbitrator.  Further, the union will provide a greater balance of power in contract negotiations, seeking what the workers want.

Employers will counter that the wages being paid are good if one makes local comparisons.  The union cannot promise any increase.  Any raise must be approved by the employer.  What is certain is the union will want to collect its dues.  The employer may talk about not needing an outsider to obtain improvements.  The managers can talk about merit being recognized over seniority.  The grievance procedure in place may be mentioned.  There is also the low road, which involves attacking the union and its leadership as crooked, shortsighted, selfish and the like.  Threats cannot be made.  However, the employer may make economic predictions of what would happen if costs are raised. The possibility of a strike taking place can also be brought up.

You asked for a source.  William H. Holley, Kenneth M. Jennings, and Roger S. Wolters (2005).  The Labor Relations Process.  Thomson-South-Western. 

Pages 169-177 deal with union security and the right-to-work.

Pages 191-232 deal with union organizing campaigns.

Virtually any other U.S. labor relations text will have similar coverage.

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Dear Magdalena You had a great answer from the previous contributor.  The erga omnes extension is of course common in Western continental Europe (in Eastern Europe, company level bargaining predominates in most countries).  In my view, the only way that unions can overcome the associated free-rider problem is by developing their offer way beyond the benefits (not always very marked benefits it must be said because the union premium in these jurisdictions is not high and normally hovers around 1% anyway).  So it becomes a question of the unions' offer to members/potential members.  In short, this is a problem faced by all unions because even where you do not have erga omnes requirement (as in the UK for example) unions have had increasingly work very hard because they are really not effective in collective wage bargaining anyway.  So it is from the Anglo-Saxon world that a wide range of ideas have developed about what trade unions' offer can and should be going beyond wage bargaining.  However, just how effective they have been is something I have written about--please take a look at McIlroy and Croucher, it is on this site.

Good luck

Richard 

Wow..this website works.....really nice¡¡¡ Thank you.

You are very welcome Magdalena 

Richard

Magdalena: Below you will find the most recent references I could find in my office. I have taught with historic editions of both of these texts.  Kenneth M. Jennings worked with me for 13 years before he passed away in 1999. He is still listed as an author on the second text.

References

Michael R. Carrell and Christina Heavrin (2010). Labor Relations and Collective Bargaining: Cases, Practice and Law, Ninth Edition. Upper Saddle River, NJ: Prentice-Hall.   Pages 131-45 deal with union organizing elections, and pages 145-154 with union security, the right-to-work and the duty of fair representation.

William H. Holley, Kenneth M. Jennings and Roger S. Wolters (2008). The Labor Relations Process, Ninth Edition.  South-Western, a part of Cengage Learning. Pages 158-166 deal with union security and the right-to-work. Pages 176-219 deal with union organizing campaigns.

Magdalena, a few of the articles in my ResearchGate deal explicitly with right to work, and Allen Ponak and I also developed a public policy submission for the Canadian province of Alberta that lists a biography of RTW effects on a variety of variables. The full text also is in ResearchGate. The studies we discuss are now old, but all of them were peer-reviewed and set in the United States. This submission to Alberta should help kick start you towards a more systematic approach to the topc.  And you need to know a lot more about the history, as Bruce Fortado's post provides. 

Article Mandatory Agency Shop Laws As an Explanation of Canada-U.S. ...

Technical Report Right to Work Study: A Submission to the Alberta Economic De...

Thank you ery much (all of you) for your help¡¡¡ Ty Daphne for your work

These responses were fascinating. In Australia, if there is a collective agreement in your workplace that sets certain wages and conditions, then everyone in the workplace gets those wages and conditions. In New Zealand, the law says that those who are members get the benefits right away, while there is a 6 month time lag for the benefits to reach those who are not members. The whole notion of RTW states is a foreign country (in every sense). I suppose that you could classify us a non-RTW country. Really appreciated your comments to Magdalena, Richard Croucher.

Thanks a lot Robin

Richard

Matías

Again, in this website, I have to say Thank You. Its amaizing ....I only expected the ciber-silence... :-)

Matías... sei italiano?..perchè per il nome e il cognome mi sembra...

Thank you