We prove an ergodic theorem for the rotation number of the composition of a sequence os stationary random homeomorphisms in S 1. In particular, the concept of rotation number of a matrix g ε G1 + (2, ℝ) can be generalized to a product of a sequence of stationary random matrices in Gl +(2, ℝ). In this particular case this result provides a counter-part of the Osseledec's multiplicative ergodic theorem which guarantees the existence of Lyapunov exponents. A random sampling theorem is then proved to show that the concept we propose is consistent by discretization in time with the rotation number of continuous linear processes on ℝ. © 2000 VSP.82175188Arnold, L., (1998) Random Dynamical Systems, , Springer-VerlagArnold, L., Scheutzow, M., Perfect cocycles through stochastic differential equations (1995) Prob. Th. Rel Fields, 101, pp. 65-88Arnold, L., San Martin, L.A., A multiplicative ergodic theorem for rotation number (1989) J. Dynamics Differential Equations, 1, pp. 95-119Crauel, H., Lyapunov exponents and invariant measures of stochastic systems on manifolds (1986) Lyapunov Exponents. Lecture Notes in Math., p. 1186. , L. Arnold and V. Wihstutz (eds.) SpringerFurstenberg, H., Kifer, Y., Random matrix products and measures on projective spaces (1983) Israel Journal of Mathematics, 46Nitecki, Z., (1971) Differentiate Dynamics-an Introduction to the Orbit Structure of Dif-feomorphisms, , The MIT PressOppenheim, A.V., Schafer, R.W., (1989) Discrete-time Signal Processing, , Prentice-HallPapoulis, A., (1984) Signal Analysis, , McGraw Hill, InternationalRuelle, D., Ergodic theory of differentiable dynamical systems (1979) I.H.E.S.-Publ. Math., 50Ruffino, P.R.C., Rotation numbers for stochastic dynamical systems (1997) Stochastics and Stochastics Reports, 60, pp. 289-318San Martin, L.A., (1988) A) Rotation Numbers of Differential Equations: A Framework in the Linear Case. Relatorio Tecnico 05/88, , Instituto de Matemdtica, UNICAMP, SP, Brazil(1988) Rotation Numbers in Higher Dimensions, , Report 199, Institute for Dynamical Systems, Bremen University, Bremen, Germany