Let $R$ be a commutative Noetherian ring, $\mathfrak{a}$ an ideal of $R,M$ and N be two finitely generated $R$-modules. Let $t$ be a positive integer. We prove that if $R$ is local with maximal ideal $\mathfrak{m}$ and $M{\otimes }_{R}N$ is of finite length then $H_{\mathfrak{m}}^t(M,N)$ is of finite length for all $t\ge 0$ and
$$l_R(H_{\mathfrak{m}}^t(M,N))\le \sum _{i=0}^t{l}_R({\mathrm{Ext}}_R^i(M,H_{\mathfrak{m}}^{t-i}(N))).$$

This yields $l_R(H_{\mathfrak{m}}^t(M,N))=l_R({\mathrm{Ext}}_R^t(M,N))$.

Additionally, we show that ${\mathrm{Ext}}_R^i(R/\mathfrak{a},N)$ is Artinian for all $i\le t$ if and only if $H_{\mathfrak{a}}^i(M,N)$ is Artinian for all $i\le t$. Moreover, we show that whenever $\dim (R/\mathfrak{a})=0$ then $H_{\mathfrak{a}}^t(M,N)$ is Artinian for all $t\ge 0$.