Abstract. The paper study counter-dependent pseudorandom number generators based on m-variate (m > 1) ergodic mappings of the space of 2-adic integers Z2. The sequence of internal states of these generators is defined by the recurrence law xi+1 = HB i (xi) mod 2n, whereas their output sequence is zi = FB i (xi) mod 2n; here xj, zj are m-dimensional vectors over Z2. It is shown how the results obtained for a univariate case could be extended to a multivariate case.