  We study the Langevin dynamics of flux lines of high--T$_c$ superconductors
in the presence of random quenched pinning. The hydrodynamic theory for the
densities is derived by starting with the microscopic model for the flux-line
liquid. The dynamic functional is expressed as an expansion in the dynamic
order parameter and the corresponding response field. We treat the model within
the Gaussian approximation and calculate the dynamic structure function in the
presence of pinning disorder. The disorder leads to an additive static peak
proportional to the disorder strength. On length scales larger than the line
static transverse wandering length and at long times, we recover the
hydrodynamic results of simple frictional diffusion, with interactions
additively renormalizing the relaxational rate. On shorter length and time
scales line internal degrees of freedom significantly modify the dynamics by
generating wavevector-dependent corrections to the density relaxation rate.
