On equicontinuity of homeomorphisms with finite distortion in the plane

It is stated equicontinuity and normality of families ${\mathfrak{F}}^{\mathrm{\Phi }}$ 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 $\int \mathrm{\Phi }(K_f(z))dxdy<\mathrm{\infty }$ in a domain $D\subset \text{C}\mathrm{.}$ It is shown that the found conditions on the function $\mathrm{\Phi }$ are not only sufficient but also necessary for equicontinuity and normality of such families of mappings.