We investigate the peculiar velocity field due to long cosmic strings in several cosmological models and analyse the influence of a nonscaling behaviour of the string network, which is expected in open cosmological models or models with a cosmological constant. It is shown that the deviation of the propability distribution of the peculiar velocity field from the normal distribution is only weak in all models. It is further argued that one can not necessarily obtain the parameter $��=��_{0}^{0.6}/b$ from density and velocity fields, where $��_0$ is the density parameter and $b$ the linear biasing parameter, if cosmic strings are responsible for structure formation in the universe. An explanation for this finding is given.

11 pages, 5 figures