  Let $D$ be a division ring with the center $F$ and $D^*$ be the
multiplicative group of $D$. In this paper we study locally nilpotent maximal
subgroups of $D^*$. We give some conditions that influence the existence of
locally nilpotent maximal subgroups in division ring with infinite center.
Also, it is shown that if $M$ is a locally nilpotent maximal subgroup that is
algebraic over $F$, then either it is the multiplicative group of some maximal
subfield of $D$ or it is center by locally finite. If, in addition we assume
that $F$ is finite and $M$ is nilpotent, then the second case cannot occur,
i.e. $M$ is the multiplicative group of some maximal subfield of $D$.
