The MAPK network is a principal component of many intracellular signaling modules. Multistability (the existence of multiple stable steady states) is considered an important property of such networks. Theoretical studies have established parameter values for multistability for many models of MAPK networks. Deciding if a given model has the capacity for multistationarity (the existence of multiple steady states) usually requires an extensive search of the parameter space. Two simple parameter inequalities will be presented. If the first inequality is satisfied, multistationarity, and hence the potential for multistability, is guaranteed. If the second inequality is satisfied, the uniqueness of a steady state, and hence the absence of multistability, is guaranteed. The method also allows for the direct computation of the total concentration values such that multistationarity occurs. Multistability in the ERK -- MEK -- MKP model will be presented. Some possible generalizations of this method will be discussed. This is a joint work with Carsten Conradi.