  In this paper we are concerned with the two-stage contact process introduced
in \cite{Krone1999} on a high-dimensional lattice. By comparing this process
with an auxiliary model which is a linear system, we obtain two limit theorems
for this process as the dimension of the lattice grows to infinity. The first
theorem is about the upper invariant measure of the process. The second theorem
is about asymptotic behavior of the critical value of the process. These two
theorems can be considered as extensions of their counterparts for the basic
contact processes proved in \cite{Grif1983} and \cite{Schonmann1986}.
