  The generalization of the ARMA time series model to the multidimensional
index set $\mathbb{Z}^d$, $d\ge2$, is called spatial ARMA model. The purpose of
the following is to specify necessary conditions and sufficient conditions for
the existence of strictly stationary solutions of the ARMA equations when the
driving noise is i.i.d. Two different classes of strictly stationary solutions
are studied, solutions of causal and non-causal models. For the special case of
a first order model on $\mathbb{Z}^2$ conditions are obtained, which are
simultaneously necessary and sufficient.
