  We present analytical results for the finite-size scaling in d--dimensional
O(N) systems with strong anisotropy where the critical exponents (e.g. \nu_{||}
and \nu_{\perp}) depend on the direction. Prominent examples are systems with
long-range interactions, decaying with the interparticle distance r as
r^{-d-\sigma} with different exponents \sigma in corresponding spatial
directions, systems with space-"time"a anisotropy near a quantum critical point
and systems with Lifshitz points. The anisotropic properties involve also the
geometry of the systems. We consider systems confined to a d-dimensional layer
with geometry L^{m}\times\infty^{n}; m+n=d and periodic boundary conditions
across the finite m dimensions. The arising difficulties are avoided using a
technics of calculations based on the analytical properties of the generalized
Mittag-Leffler functions.
