  The method of \emph{random integral representation}, that is, the method of
representing a given probability measure as the probability distribution of
some random integral, was quite successful in the past few decades. In this
note we will find such a representation for generalized s-selfdecomposable and
selfdecomposable distributions that have the \emph{factorization property}.
These are the classes $\mathcal{U}^f_{\be}$ and $L^f$, respectively
