A method is presented for the construction of unitary representations of semisimple Lie groups (or, more precisely, of the corresponding algebras), proceeding directly from the commutation relations among the canonical generators e±α and hα. In the case of the orthogonal groups, the correspondence between the canonical generators and the more usual tensor generators is written down explicitly. It is shown how this method can be used to construct a certain class of representations (bounded above or below) of the Lie algebras of the noncompact groups SU(p, q) and SO(p, q), which arise in the dynamical group treatment of certain physical systems.