spaces $(E_\Phi^q)_t(\rn)$, we first introduce the Orlicz-slice Hardy spaces, $(HE_\Phi^q)_t(\rn)$, which are defined via the radial maximal functions (see Definition \[dh\] below) and then present some fundamental properties of these Orlicz-slice Hardy spaces $(HE_\Phi^q)_t(\rn)$ including characterizations via the grand and the non-tangential maximal functions (see Theorem \[mdj\] below), the poisson integral (see Theorem \[poisson\] below), the atom (see Theorem \[atom ch\] below), the molecule (see Theorem \[molecular\] below), the Littlewood-Paley functions (see Theorems \[lusin\], \[gfunction\] and \[glamda\] below) and the finite atomic decomposition (see Theorem \[finite\] below). We also clarify the relations between $(E_\Phi^q)_t(\rn)$ and $(HE_\Phi^q)_t(\rn)$ in Theorem \[dayu1\] below.

The proofs of all main results in Section \[s3\] are given in Section \[s4\]. Recall that a real-variable theory of Hardy spaces related to ball quasi-Banach function spaces was recently developed in [@ykds]. The results obtained in [@ykds] are of so wide generality that, in Section \[s4\], we can directly apply them to obtain the atomic and the molecular characterizations as well as those characterizations via various maximal functions, the Poisson integral and the Lusin area function of the Orlicz-slice Hardy space $(HE_\Phi^q)_t(\rn)$ as well as the relation between $(HE_\Phi^q)_t(\rn)$ and $(E_\Phi^q)_t(\rn)$. Then, using the atomic characterization, we further establish 