Cellular neural/nonlinear networks (CNNs) are analog dynamic processor arrays, that present local interconnections. CNN models with polynomial interactions among the cells (Polynomial type CNNs) have been recently introduced. They are useful for solving some complex computational problems and for real-time implementation of PDE-based algorithms. This manuscript provides some simple and rigorous sufficient conditions for stability of polynomial type CNNs. A particular emphasis is given to conditions that can be expressed in terms of template elements, since they can be exploited for design purposes.