  Assume $R$ is a local Cohen-Macaulay ring. It is shown that $\Ass_R
(H^l_I(R))$ is finite for any ideal $I$ and any integer $l$ provided $\Ass_R
(H^2_{(x,y)}(R))$ is finite for any $x,y\in R$ and $\Ass_R
(H^3_{(x_1,x_2,y)}(R))$ is finite for any $y\in R$ and any regular sequence
$x_1,x_2\in R$. Furthermore it is shown that $\Ass_R (H^l_I(R))$ is always
finite if $\dim (R)\leq 3$. The same statement is even true for $\dim (R)\leq
4$ if $R$ is almost factorial.
