  Let $\fa$ denote an ideal of a commutative Noetherian ring $R$ and $M$ and
$N$ two finitely generated $R$-modules with $\pd M< \infty$. It is shown that
if $\fa$ is principal or $R$ is complete local and $\fa$ a prime ideal with
$\dim R/\fa=1$, then the generalized local cohomology module $H^i_{\fa}(M,N)$
is $\fa$-cofinite for all $i \geq 0$. This provides an affirmative answer for
the above ideal $\fa$ to a question proposed in [{\bf 13}].
