  A slight modification of the Kontorovich-Lebedev transform is an automorphism
on the vector space of polynomials. The action of this $KL_{\alpha}$-transform
over certain polynomial sequences will be under discussion, and a special
attention will be given the d-orthogonal ones. For instance, the Continuous
Dual Hahn polynomials appear as the $KL_{\alpha}$-transform of a 2-orthogonal
sequence of Laguerre type. Finally, all the orthogonal polynomial sequences
whose $KL_{\alpha}$-transform is a $d$-orthogonal sequence will be
characterized: they are essencially semiclassical polynomials fulfilling
particular conditions and $d$ is even. The Hermite and Laguerre polynomials are
the classical solutions to this problem.
