  Let $D$ be a division ring with center $F$, and $G$ an almost subnormal
subgroup of $D^*$. In this paper, we show that if $G$ contains a non-abelian
locally solvable maximal subgroup, then $D$ must be a cyclic algebra of prime
degree over $F$. Moreover, it is proved that every locally nilpotent maximal
subgroup of $G$ is abelian.
