Parametric difference linear systems of the form \[ G(n+ 1,\alpha)= B(\alpha)G(n,\alpha),\quad n\geq 0,\quad\alpha> 0,\quad G(0,\alpha)= G(0), \] arise in the stability analysis of finite difference schemes, where \(B(\alpha)\) and \(G(n,\alpha)\) are \(s\times s\) matrices, and \(\alpha\) is a positive parameter. The authors provide sufficient conditions for the uniform stability and for the fixed-station stability in the general case of an \(s\times s\) matrix \(B(\alpha)\) and in the special cases \(B(\alpha)= (I + \alpha A)^{-1}(I- \alpha A)\) and \(B(\alpha)= (I -\alpha A)^{-1}(I+ \alpha A)\) which arise from \(\theta\)-integration schemes (e.g. Crank-Nicolson scheme).