  Using a generalized response theory we derive the electronic Raman response
function for metals with anisotropic relaxation rates. The calculations account
for the long--range Coulomb interaction and treat the collision operator within
a charge conserving relaxation time approximation. We extend earlier treatments
to finite wavenumbers ($|{\bf q}|\ll k_{\rm F}$) and incorporate inelastic
electron--electron scattering besides elastic impurity scattering. Moreover we
generalize the Lindhard density response function to the Raman case. Numerical
results for the quasiparticle scattering rate and the Raman response function
for cuprate superconductors are presented.
