  We introduce elliptic and parabolic $\mathcal{B}_{1}$ classes that generalize
the well-known $\mathfrak{B}_{p}$ classes of DeGiorgi, Ladyzhenskaya and
Ural'tseva with $p>1$. New classes are applied to prove pointwise continuity of
solutions of elliptic and parabolic equations with nonstandard growth
conditions. Our considerations cover new cases of variable exponent and $(p,
q)$-phase growth including the ,,singular-degenerate'' parabolic case $p<2<q$.
