  The present paper is devoted to the study of space mappings, which are more
general than quasiregular mappings. The questions of the behavior of
differentiable mappings having the so--called $N,$ $N^{-1},$ $ACP$ and
$ACP^{-1}$ -- properties are studied in the work. Under some additional
conditions, it is showed that the modulus of such mappings $f$ can be more than
each degree of logarithmic function at every neighborhood of the isolated
essential singularity of $f.$
