It is well known that generalized Walsh functions can be considered as characters of Vilenkin groups (see, e.g., [6], [11]). For wavelets on Vilenkin groups most of the results relate to the locally compact group G p , which is defined by a fixed integer p ≥ 2 (the case p = 2 corresponds to the Cantor group). In this paper, we are interested in an nonstationary MRA and related wavelets for the space L2(G p ); for the stationary case see [2], [4], [5], and references therein. Furthermore, we give an algorithm for construction of nonstationary wavelets on the Vilenkin group associated with a sequence {p j } j=1 ∞, p j ≥ 2, of natural numbers.