  A discrete set $A$ in the Euclidian space is almost periodic if the measure
with the unite masses at points of the set is almost periodic in the weak
sense. We investigate properties of such sets in the case when $A-A$ is
discrete. In particular, if $A$ is a Bohr almost periodic set, we prove that
$A$ is a union of a finite number of translates of a certain full--rank
lattice. If $A$ is a Besicovitch almost periodic set, then there exists a
full-rank lattice such that in most cases a nonempty intersection of its
translate with $A$ is large.
