The traveling wave problem for a viscous conservation law with a
nonlinear source term leads to a singularly perturbed problem
which necessarily involves a non-hyperbolic point. The correponding
slow-fast system indicates the existence of canard solutions which
follow both stable and unstable parts of the slow manifold.
In the present paper we show that for the viscous equation there
exist such heteroclinic waves of canard type. Moreover, we determine
their wave speed up to first order in thesmall viscosity parameter
by a Melnikov-like calculation after a blow-up near the non-hyperbolic
point. It is also shown that there are discontinuous waves of the
inviscid equation which do not have a counterpart in the viscous case.