  We study a new non-equilibrium dynamical model: a marked continuous contact
model in $d$-dimensional space ($d \ge 3$). We prove that for certain values of
rates (the critical regime) this system has the one-parameter family of
invariant measures labelled by the spatial density of particles. Then we prove
that the process starting from the marked Poisson measure converges to one of
these invariant measures. In contrast with the continuous contact model studied
earlier in \cite{KKP}, now the spatial particle density is not a conserved
quantity.
