Summary: This paper is a direct sequel to the authors’ paper in ibid. 7, No. 1, 107–124 (2000; Zbl 0945.33007). The present part deals with the problem of finding all \(d\)-orthogonal polynomial sets generated by \(G(x,t)= e^t\Psi(xt)\). The resulting polynomials reduce to Laguerre polynomials for \(d= 1\) and to two-orthogonal polynomials associated with MacDonald functions for \(d= 2\), recently considered by the authors [Methods Appl. Anal. 7, No. 4, 641–662 (2000; Zbl 1009.33014)] and by W. Van Assche and S. B. Yakubovich [Integral Transforms Spec. Funct. 9, No. 3, 229–244 (2000; Zbl 0959.42016)]. Various properties for the obtained polynomials are singled out.