  The mechanical response of active media ranging from biological gels to
living tissues is governed by a subtle interplay between viscosity and
elasticity. In this Letter, we generalize the canonical Kelvin-Voigt and
Maxwell models to active viscoelastic media that break both parity and
time-reversal symmetries. The resulting continuum theories exhibit viscous and
elastic tensors that are both antisymmetric, or odd, under exchange of pairs of
indices. We analyze how these parity violating viscoelastic coefficients
determine the relaxation mechanisms and wave-propagation properties of odd
materials.
