The aim of this work is to show an abstract framework to analyze the family of linear degenerate parabolic problems and family of linear degenerate parabolic mixed problems. To linear degenerate parabolic mixed equations, we deduce sufficient conditions to existence and uniqueness of solution by combining the theory for the degenerate parabolic equations and the classical Babuska-Brezzi theory. The numerical approximation was made through the finite element method in space and a Backward-Euler scheme in time. To degenerate parabolic and degenerate parabolic mixed problems, we obtain sufficient conditions to ensure that the fully-discrete problem has a unique solution and to prove quasi-optimal error estimates for the approximation. Moreover, we present a degenerate parabolic problem which arises from electromagnetic applications and deduce its well-posedness and convergence by using the developed abstract theory, including numerical tests to illustrate the performance of the method and confirm the theoretical results. Finally, we present the linear degenerate parabolic mixed (0 g) equations. We deduce that the fully-discrete problem has a unique solution and prove quasi-optimal error estimates for the approximation.