Degenerate and singular abstract differential equations are considered via the operational method by G. Da Prato and P. Grisvard. The approach should permit one to treat different types of equations, but emphasis here is placed on the parabolic case. The conditions to be assumed concerning both regularity and operator bundles seem stronger than the ones in other papers on the subject, but it has to be noted that here strict or strong solutions are looked for. The last section is devoted to some examples of applications to partial differential equations.