The dynamics of tilted vortex lines in Josephson-coupled layered super
conductors is considered within the time-dependent Ginzburg-Landau the
ory. The frequency and angular dependences of the complex-valued vorte
x mobility mu are studied. The components of the viscosity and inertia
l mass tensors are found to increase essentially for magnetic field or
ientations close to the layers. For superconducting/normal metal multi
layers the frequency (omega) range is shown to exist where the mu(-1)
value depends logarithmically on omega.