  We consider Markov processes in continuous time with state space $\posint^N$
and provide two sufficient conditions and one necessary condition for the
existence of moments $E(\|X(t)\|^r)$ of all orders $r \in \nat$ for all $t \geq
0$. The sufficient conditions also guarantee an exponential in time growth
bound for the moments. The class of processes studied have finitely many state
independent jumpsize vectors $\nu_1,\dots,\nu_M$. This class of processes arise
naturally in many applications such as stochastic models of chemical kinetics,
population dynamics and queueing theory for example. We also provide a
necessary and sufficient condition for stochiometric boundedness of species in
terms of $\nu_j$.
