In this paper a generalized parametric equation (1) \(0\in f(p,x)+N(x)\), where \(f\) is a given function from \(\Omega\times \mathbb{R}^ n\) to \(\mathbb{R}^ m\), \(N\) a multifunction from \(\mathbb{R}^ n\) to \(\mathbb{R}^ m\), and \(p\) an element of an open subset \(\Omega\) of a normed linear space, is considered. The aim of the paper is to find conditions which guarantee a certain kind of stability properties of solution sets if the parameter \(p\) varies near its fixed value \(\bar p\). Special cases of the equation (1) are considered separately and an application to sensitivity analysis in mathematical programming is presented.