We study the problem of upper semicontinuity of compact global attractors of non-autonomous dynamical systems for small perturbations. For the general nonautonomous dynamical systems, we give the conditions of upper semicontinuity of attractors for small parameter. Several applications of these results are given (quasihomogeneous systems, monotone systems, nonautonomously perturbed systems, nonautonomous 2D Navier-Stokes equations and quasilinear functional-differential equations).