  We study the boundedness of intrinsic square functions and their commutators
on generalized Orlicz-Morrey spaces $M^{\Phi,\varphi}(\mathbb{R}^n)$. In all
the cases the conditions for the boundedness are given either in terms of
Zygmund-type integral inequalities on weights $\varphi(x,r)$ without assuming
any monotonicity property of $\varphi(x,r)$ on $r$.
