LetGbe a real connected semisimple real Lie group and let beAa connected reductive subgroupg,athe complexified Lie algebras ofGand A respectively; assume (g,a) is a regular pair.In this paper we study general properties of (g, A)-modules, and we prove for two particular cases that every admissible (g, A)-module with an infinitesimal character has finite length.We also compute Gelfand-Kiriilov dimensions for some modules and a number (Vogan's dimension) related to it.Finally we construct a virtual (g,A)-module with“minimal”Vogan's dimension.