  The Zeldovich approximation is applied to study the accretion of hot and cold
dark matter onto moving long strings. It is assumed that such defects carry a
substantial amount of small-scale structure, thereby acting gravitationally as
a Newtonian line source whose effects dominate the velocity perturbations.
Analytical expressions for the turn-around surfaces are derived and the mass
inside of these surfaces is calculated. Estimates are given for the redshift
dependence of $\Omega_{nl}$, the fraction of mass in nonlinear objects.
Depending on parameters, it is possible to obtain $\Omega_{nl} = 1$ at the
present time. Even with hot dark matter, the first nonlinear filamentary
structures form at a redshift close to 100, and there is sufficient nonlinear
mass to explain the observed abundance of high redshift quasars and damped
Lyman alpha systems. These results imply that moving strings with small-scale
structure are the most efficient seeds to produce massive nonlinear objects in
the cosmic string model.
