  We study travelling fronts of equations of the form $u_{tt} + \phi(u) u_x =
u_{xx} + f(u)$. A criterion for the transition from linear to nonlinear
marginal stability is established for positive functions $\phi(u)$ and for any
reaction term $f(u)$ for which the usual parabolic reaction diffusion equation
$u_t = u_{xx} + f(u)$ admits a front. As an application, we treat reaction
diffusion systems with transport memory.
