  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 $\beta=\Omega_{0}^{0.6}/b$ from density and velocity
fields, where $\Omega_0$ 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.
