Abstract
In this paper we first construct an analytic realization of the C-lambda-extended oscillator algebra with the help of difference-differential operators. Secondly, we study families of d-orthogonal polynomials which are extensions of the Hermite and Laguerre polynomials. The underlying algebraic framework allowed us a systematic derivation of their main properties such as recurrence relations, difference-differential equations, lowering and rising operators and generating functions. Finally, we use these polynomials to construct a realization of the C-lambda-extended oscillator by block matrices.