An algebra with a type $\Omega$ and a carrier $A$ is an $\Omega$-subalgebra of a semigroup $S$ if $A\subseteq S$ and if there is a mapping $\omega\to\bar\omega$ of $\Omega$ into $S$ such that $\omega(a_1,\dots,a_n)=\bar\omega a_1\dots a_n$, for every $n$-ary operator $\omega\in\Omega$ and the sequence of elements $a_1,\dots,a_n$ of $A$. If $\underline C$ is a class of semigroups then by $\underline C(\Omega)$ is denoted the class of $\Omega$-algebras (i.e. algebras of the type $\Omega$) which are subalgebras of semigroups belonging to $\underline C$. It is well known (see [l] p.\,185 or [4] p.\,78) that SEM($\Omega$) is the class of all $\Omega$-algebras. It is also known [5] that ABSEM($\Omega$) is a variety. The object of our investigations is the set $V$ of varietis $\underline V$ of semigroups such that $\underline V(\Omega)$ is also a variety. In Theorem 1. of this paper we show that $\underline C_{r,m}(\Omega)$ is a variety only if $r=1$ or $\Omega$ does not contain $n$-ary operators for $n\geq 2$, where $\underline C_{r,m}$ is the class of commutative semigroups which satisfy the law $x^r=x^{r+m}$.