In [1] are considered so called \emph{semiprimary} semigroups. H. Lal, [2] also considered semiprimary semigroups. But the concept of H. Lal has another sense. In this paper we introduce the concept of $r$-semigroups ($S$ is an $r$-\emph{semigroup} iff the radical of every ideal of $S$ is an ideal) and the interrelations of the class of semipimary semigroups and the class of semiprimary semigroups ($r$-\emph{semiprimary}) in the sense of H. Lal are given.