What is the problem of the internal thoracic artery that feeds the mammary, when precontracted with NE and ANG II that leads to wobbling of the curve as you see in the attachment images.
As Ismail says, preconditioning before the experiment by challenging with 80 mM [K] (isotonic substitution for Na+) for 5 mins a couple of times often helps stabilising vascular preparations. However, I am not sure that the oscillations you are seeing really count as a "problem" - except to the experimenter - as they are very common in isolated arteries depending on type. Mesenteric arteries often exhibit the same sort of response to agonists. People often just don't show it in publications!
Apart from the high[K+] challenge, you may be able to minimise this by 1) being very careful not to over-stretch the artery whilst tying up, 2) by carefully removing as much adventitia as possible, and 3) by leaving the preparation to equilibrate after tying up for 30- 60 min before starting the experiment. Some artery types just seem to be more twitchy than others (it is not a problem generally in pulmonary artery, but is in mesenteric).
We used to call this spontaneous activity and Dr Ward is absolutely right; it is really not a problem as long as you are able to quantify changes in vessel tone.
I remember on the other hand that mesenteric arteries (rat, rabbit, mouse, dog etc) actually show this type of 'behaviour' even at basal tone (i.e. without being pre-contracted with NE, Ang II or KCl).
Are these helicoidal strips and which physiological buffer are you using? In addition, if you want to reduce these oscillations at least with an alpha agonist, try methoxamine instead and add indomethacin in your assay buffer. The addition of an inexpensive betablocker may also help.
It will be good to know the doses of agonists at which you observe these oscillations - some arteries have intrinsic rhythmic activity which are exaggerated by low doses of agonists. Inadequate rinsing/oxygenation during equilibration may also result in accumulation of metabolites which induce rhythmic contractions. Jeremy Ward's KCL suggestion is also useful. You may also try in-vitro chemical denervation of your tissues using 6-hydroxydopamine.
I think Prof Ward has summed it up, this is normal behaviour of healthy arteries, and the steps recommended can reduce this. If this is a major problem for you trying alternative constrictor such as U46619 (thromboxane mimetic) may lead to a more stable constriction (it generally does in my lab) but in some peoples hands is reported to affect the vasodilatation seen.