E. C. Lance has recently extended the Birkhoff ergodic theorem to noncommutative dynamical systems. Using Lance's result, we extend the random ergodic theorem of H. R. Pitt, S. M. Ulam, S. Kakutani and J. von Neumann to noncommutative context. Introduction and notations. E. C. Lance has recently proved a beautiful extension of Birkhoff ergodic theorem to von Neumann algebra context (cf. [5]). Since then, several classical almost everywhere pointwise convergence theorems have been extended to von Neumann algebras (cf. [1, 2, 6]). In this paper we use Lance's results to prove an extension of the random ergodic theorem of H. R. Pitt, S. M. Ulam and J. von Neumann (cf. [7, 9]). Our proof follows from that of S. Kakutani (cf. [4]) and Ryll-Nardzewski (cf. [8]). We fix a pair (C, p) where e is a von Neumann algebra and p is a faithful normal state on e. As in the commutative case, we call a kernel a positive linear contraction T of ef into itself such that TI = 1, p(Ta) = p(a), p((Ta)*T(a)) 0, there exists a projection e of ef such that p(e) 1E and limnII(a an)e = 0 (when e is commutative, e = L(X, ,i), with (X, y) a probability space, this convergence coincides, via Egorov's theorem, with the almost everywhere pointwise convergence). Let (X, ,i) be a probability space, for each x C X we associate an automorphism Tx of C leaving p invariant and we assume that for every a C e, the mapping X 3 x Txa C f e) & 2 ( Z,P) ). THEOREM 1. For every a C e, there exists aO F (Y such that for v-almost every (xl, x2,...) in XN we have n nEl TXkTXkI. .. *Tla I a0 p-almost uniformly as n -oo. Furthermore aO is Tx-invariant for ,i-almost every x in X. Received by the editors November 20, 1981. AMS (MOS) subject classifications (1970). Primary 46L10; Secondary 28A65.