Let ( G , V ) be a regular prehomogeneous vector space (abbreviated to P V ), where G is a reductive algebraic group over ℂ . If V = ⊕ i = 1 n V i is a decomposition of V into irreducible representations, then, in general, the PV’s ( G , V i ) are no longer regular. In this paper we introduce the notion of quasi-irreducible P V (abbreviated to Q -irreducible), and show first that for completely Q -reducible P V ’s, the Q -isotypic components are intrinsically defined, as in ordinary representation theory. We also show that, in an appropriate sense, any regular PV is a direct sum of Q -irreducible P V ’s. Finally we classify the Q -irreducible PV’s of parabolic type.