Starting from the effective action for the order parameter (i.e., the generalization of the phase Hamiltonian), the generating functional governing the real-time dynamics is derived within the Keldysh formalism. As a particular advantage of this technique, it is possible to perform the average over the random (impurity) pinning potential at an early stage---this leads to an ``interaction'' term in the action that has peculiar time correlations. We study explicitly results in second order in the impurity-pinning potential with emphasis on the nonlinear response to a static field (the sliding mode) in two and three dimensions including the experimentally interesting crossover region. We study also the effect of thermal fluctuations for three- and two-dimensional situations and, as an example, describe how long-range Coulomb forces, which are screened by the normal electrons, can be incorporated.