Siberian Federal University

Let K = D+ ∪T ∪D− be an n-circled two-sided wedge in C wherethe unitpolycircle(torus) T plays a role of the edge, and domains D± adjoined to T may not contain any full-dimensional cone near T . In this case we say that the wedge K is in nongeneral position. Consider a question when the closures of pure n-dimensional analytic sets A± ⊂ D± × C compose a single analytic set in a neighborhood of the wedge K × C . If K is in general position then the answer to the question is given by the theorem of S.I.Pinchuk. In the present article we expand this theorem to the case when the two-circled wedge K is in nongeneral position, and m =1.