  Let $\fa$ be an ideal of a local ring $(R,\fm)$ and $M$ a finitely generated
$R$-module. We investigate the structure of the formal local cohomology modules
${\vpl}_nH^i_{\fm}(M/\fa^n M)$, $i\geq 0$. We prove several results concerning
finiteness properties of formal local cohomology modules which indicate that
these modules behave very similar to local cohomology modules. Among other
things, we prove that if $\dim R\leq 2$ or either $\fa$ is principal or $\dim
R/\fa\leq 1$, then $\Tor_j^R(R/\fa,{\vpl}_nH^i_{\fm}(M/\fa^n M))$ is Artinian
for all $i$ and $j$. Also, we examine the notion $\fgrade(\fa,M)$, the formal
grade of $M$ with respect to $\fa$ (i.e. the least integer $i$ such that
${\vpl}_nH^i_{\fm}(M/\fa^n M) \neq 0$). As applications, we establish a
criterion for Cohen-Macaulayness of $M$, and also we provide an upper bound for
cohomological dimension of $M$ with respect to $\fa$.
