Groups with $\pi$-minimal and $\pi$-layer minimal conditions. II

For an arbitrary set $\pi$ of prime numbers we study the properties and structure of groups satisfying the $\pi$-minimal and $\pi$-layer minimal conditions. In particular, we describe the structure of the almost $RN$-groups (and thereby that of the locally solvable groups) with these conditions. Under the assumption $2\in\pi$, we describe the structure of locally graded groups (and thereby that of locally finite groups) with these conditions.