  Let $E$ be a subset of positive integers such that
$E\cap\{1,2\}\ne\emptyset$.
  A weakly mixing finite measure preserving flow $T=(T_t)_{t\in\Bbb R}$ is
constructed such that the set of spectral multiplicities (of the corresponding
Koopman unitary representation generated by $T$) is $E$. Moreover, for each
non-zero $t\in\Bbb R$, the set of spectral multiplicities of the transformation
$T_t$ is also $E$. These results are partly extended to actions of some other
locally compact second countable Abelian groups.
