Generalized random processes by various types of continuity are considered and classified as generalized random processes (GRPs) of type (I) and (II). Structure theorems for Hilbert space valued generalized random processes are obtained: Series expansion theorems for GRPs (I) considered as elements of the spaces $\mathcal L(\mathcal A,S(H)_{-1})$ are derived, and structure representation theorems for GRPs (II) on $K\{M_p\}(H)$ on a set with arbitrary large probability are given.