Let $(R,\fm)$ be a Noetherian local ring, $\fa$ a proper ideal of $R$, and $M$, $N$ two finitely generated $R$-modules of finite projective dimension $m$ and of finite dimension $n$, respectively. It is shown that if $n\leq 2$, then the generalized local cohomology module $H_{\fa}^{m+n}(M,N)$ is a co-Cohen-Macaulay module. Additionally, we show that $H_{\fa}^i(M,N)=0$ for all $i>m+s$ and $H_{\fa}^{m+s}(M,N)\cong\Ext_R^m(M,H_{\fa}^s(N))$ where $s$ is the cohomological dimension of $N$ with respect to $\fa$.
