Semi-crossed products of finite-dimensional C*-algebras have been characterized as a direct sum;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI);of semi-simple Banach algebras. The characterization was obtained by means of a thorough analysis of the algebras B(,K) (CRTIMES) M(,N) and of their ideal structure;Necessary and sufficient conditions were given for two semi-crossed products of finite-dimensional C*-algebras, Z('+) x (,(alpha)) and Z('+) x (,(beta)) , to be isomorphic.