Is it a contract or an "assignment?"  They're a little different. A contract states future promises, where an assignment is a present (and by the time anyone is reading it, past) transfer.

When I need to amend a contract,. the amendment paper states an entire new paragraph --

Paragraph 6.2 is replaced as follows:

6.2 Buyer shall blah blah

If I need to amend a past assignment, then I usually do an entire new document, an assignment nunc pro tunc.  An assignment nunc pro tunc states the new assignment, states that the previous document is a nullity, and the new document takes effect from the date of the old document.

thank you dear David. the  original contract(between A and C )  is under English law. in an addendum the mentioned sentence (A is replaced with B in contract X) is agreed on. the non-assigning party (C) believe that A`s rights are not transfered thereby and consequently B can not sue against C. 

I cannot opine on U.K. law.

In most U.S. states (contract law is under 51 state laws, there is no such thing a "U.S. contract law"), the usual rule is that a contract can be assigned. To remove any ambiguity, most American contracts state "this contract is binding on successors and assigns," to make clear that the contract can be assigned.

One exception is if the performance is somehow personal to the party (for example, one opera singer cannot unilaterally ask a friend to fill in).

A second exception is if there is a "no assignment" or "no assignment without consent of the other party" clause.

If there's a history of C accepting performance from B, then it's going to be hard for C to argue that now that C has breached, that B cannot enforce rights attached thereto.  However, if C refused performance from B right at the outset, then C might have a case.

I do not know UK law, but in general substituting a party is not exactly equivalent to an assignment, though in the end the difference may have no significance in most instances.  If A assigns all of A's rights under the contract to B, that is the standard assignment.  A remains bound on the contract to C.  If, however, B is substituted for A, then A is no longer bound and the new contract (a novation) is directly between B and C.  Typically a contract will allow or disallow an assignment of rights and obligations.  A novation essentially becomes a new, replacement contract with the new agreement between B and C with all rights and duties running between B and C with A out of the picture.  One must also take some care to separate rights from duties.  A can perhaps assign rights, but still be obligated to C as to duties which B does not undertake.  

So, no, a substitution of parties is not, under general contract law in the United States, an assignment.  

Again, I do not know UK law, but I suspect on this one point it is similar, though it probably has some technical refinements that may matter in some settings.

Assignment of a contract isn't really the correct way to think of the issue in English law. A party can assign the benefit (unless its a personal contract or there is a prohibition on assignment for some reason) but cannot assign the obligation without involving the other party. The involvement of the other party means we are really talking about novation, which should really take place in separate novation agreement.

Putting my Practitioner (Barrister), rather than academic, hat on this doesn't seem like an idle academic question to me. The parties should take specialist legal advice, this a complex area of English Law