The estimation of multivariate stochastic regression Y=r(X1,X2,…Xd)+ε; d≥ for a stationary random process {Xi} using wavelet methods is considered. Uniform rates of almost sure convergence over compact subsets of Rd in the Besov space Bspq are established for strongly mixing processes. Also, considering the case d=1, the results given by Doosti et al. (2008) are obtained as special cases.