  Let $R$ be a commutative noetherian ring, $\fa$ an ideal of $R$ and $M,N$
finite $R$--modules. We prove that the following statements are equivalent.
\begin{enumerate} \item[(i)] $\lc^{i}_{\fa}(M,N)$ is finite for all $i< n$.
\item[(ii)] $\Coass_R(\lc^{i}_{\fa}(M,N)) \subset \V{(\fa)}$ for all $i< n$.
\item[(iii)] $\lc^{i}_{\fa}(M,N)$ is coatomic for all $i< n$. \end{enumerate}
If $\pd M$ is finite and $r$ be a non-negative integer such that $r>\pd M$ and
$\lc^{i}_{\fa}(M,N)$ is finite (resp. minimax) for all $i\geq r$, then
$\lc^{i}_{\fa}(M,N)$ is zero (resp. artinian) for all $i\geq r$.
