  Single crystals of DyRh$_2$Si$_2$ and HoRh$_2$Si$_2$ were investigated by
thermal expansion and magnetostriction. The different types of magnetic order
can clearly be seen in these measurements, particularly the canting of the
moments away from the crystallographic $c$ direction below about 12~K and the
spin-flip for magnetic field applied along the $c$ direction. For
HoRh$_2$Si$_2$, an additional transition just below $T_{\rm N}$ is analyzed by
means of the Gr\"{u}neisen ratio and is likely caused by a change of the
magnetic structure. Our results nicely corroborate findings from other magnetic
and thermodynamic measurements on these materials and provide further evidence
suggesting the formation of magnetic domains.
