  We determine the algebraic structure of the multiplicative loops for locally
compact $2$-dimensional topological connected quasifields. In particular, our
attention turns to multiplicative loops which have either a normal subloop of
positive dimension or which contain a $1$-dimensional compact subgroup. In the
last section we determine explicitly the quasifields which coordinatize locally
compact translation planes of dimension $4$ admitting an at least
$7$-dimensional Lie group as collineation group.
