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The Gruenberg-Kegel graph $\Gamma(G)$ of a finite group $G$ is the graphwhose vertex set is the set of prime divisors of $|G|$ and in which twodistinct vertices $r$ and $s$ are adjacent if and only if there exists anelement of order $rs$ in $G$.  A finite group $G$ is called almost recognizable (by Gruenberg-Kegel graph)if there is only finite number of pairwise non-isomorphic finite groups havingGruenberg-Kegel graph as $G$. If $G$ is not almost recognizable, then it iscalled unrecognizable (by Gruenberg--Kegel graph).  Recently P.J. Cameron and the first author have proved that if a finite groupis almost recognizable, then the group is almost simple. Thus, the question ofwhich almost simple groups (in particular, finite simple groups) are almostrecognizable is of prime interest. We prove that every finite simpleexceptional group of Lie type, which is isomorphic to neither${^2}B_2(2^{2n+1})$ with $n\geq1$ nor $G_2(3)$ and whose Gruenberg-Kegel graphhas at least three connected components, is almost recognizable. Moreover,groups $ {^2}B_2(2^{2n+1})$, where $n\geq1$, and $G_2(3)$ are unrecognizable.

On characterization by Gruenberg-Kegel graph of finite simple exceptional groups of Lie type