As the authors show, a large class of models for flow in partially fissured porous media lead to abstract evolution equations of the form \[ {d\over dt} A \bigl(u(t) \bigr)+ B \bigl(u(t) \bigr) \ni f(t), \] where \(A\) is a subgradient and \(B\) is maximal monotone on a product of three Hilbert spaces. The operator \(A\) is not necessarily compact in all its components, and this allows to analyze also problems related to fluid flows in fractured media. The existence and uniqueness of solutions for the Cauchy problem are established and sufficient conditions for continuous dependence of the solutions are given.