  The notion of weakly Laskerian modules was introduced recently by the
authors. Let $R$ be a commutative Noetherian ring with identity, $\fa$ an ideal
of $R$, and $M$ a weakly Laskerian module. It is shown that if $\fa$ is
principal, then the set of associated primes of the local cohomology module
$H_{\fa}^i(M)$ is finite for all $i\geq 0$. We also prove that when $R$ is
local, then $\Ass_R(H_{\fa}^i(M))$ is finite for all $i\geq 0$ in the following
cases: (1) $\dim R\leq 3$, (2) $\dim R/\fa\leq 1$, (3) $M$ is Cohen-Macaulay
and for any ideal $\fb$, with $l=\grade(\fb,M)$,
$\Hom_R(R/\fb,H_{\fb}^{l+1}(M))$ is weakly Laskerian.
