Аннотация:We prove that the solution of the oblique derivative parabolic problem in a noncylindrical domain Omega(T) belongs to the anisotropic Holder space C-2+alpha,C- 1+alpha/2 (<(Omega)over bar>(T)), 0 < alpha < 1, even if the nonsmooth "lateral boundary" of Omega(T) is only of class C-1+alpha,C-(1+alpha/2). As a corollary, we also obtain an a priori estimate in the Holder space C2+alpha(<(Omega)over bar>(o)) for a solution of the oblique derivative elliptic problem in a domain Omega(o) whose boundary belongs only to the classe C1+alpha. (C) Academie des Sciences/Elsevier, Paris.