  It is stated equicontinuity and normality of families $\frak{F}^{\Phi}$ of
the so--called homeomorphisms with finite distortion on conditions that
$K_{f}(z)$ has finite mean oscillation, singularities of logarithmic type or
integral constraints of the type $\int\Phi\left(K_{f}(z)\right)dx\,dy<\infty$
in a domain $D\subset{\C}.$ It is shown that the found conditions on the
function $\Phi$ are not only sufficient but also necessary for equicontinuity
and normality of such families of mappings.
