  A crossover from $d$ to $d-1$, and then back to $d$-dimensional critical
behavior is argued to be a generic feature characterizing ordering in a
$d$-dimensional superlattice composed of atomically {\em thick} films of two
ferromagnets. The crossover leads to anomalous changes in the amplitudes of
critical singularities. In $d=3$ Heisenberg and $XY$ superlattices large scale
critical fluctuations persist over a wide temperature range.
