section we investigate the asymptotic behavior of $p(x_{0},\Delta_{1},t,\Delta)$ and $p(t,\Delta)$ when $t{\to}\infty$.\
**Theorem 9.2.** *Let the considered Levy process have the continuous density and let the corresponding quasi-potential $B$ be regular and strongly sectorial. And let the operator $B$ have a point of the spectrum different from zero. Then the asymptotic equality* $$p(t,\Delta)=e^{-t/\lambda_{1}}[q(t)+o(1)],\quad t{\to}+\infty$$*is true. The function $q(t)$ has the form* $$q(t)=c_{1}+\sum_{k=2}^{m}c_{k}e^{it\nu_{k}}{\geq}0,$$ *where $\nu_{k}$ are real*\
*Proof.* The spectrum $(\lambda_{k},\quad k>1)$ of the operator $B$ is situated in the sector $$-\frac{\pi}{2}\beta{\leq}\mathrm{arg}z{\leq}\frac{\pi}{2}\beta,\quad 0{\leq}\beta<1,
\quad |z|{\leq}\lambda_{1}.$$We introduce the domain $D_{\epsilon}$: $$-\frac{\pi}{2}(\beta
+\epsilon){\leq}\mathrm{arg}z{\leq}\frac{\pi}{2}(\beta
+\epsilon),\quad |z-(1/2)\lambda_{1}|<(1/2)(\lambda_{1}
-r),$$ where $0<\epsilon<1-\beta),\quad r<\lambda_{1}$. If $z$ belongs to the domain $D_{\epsilon}$ then the relation $$\mathrm{Re}(1/z)>1/\lambda_{1}$$ holds. As the operator $B$ is compact only a finite number of eigenvalues $\lambda_{k}, \quad 1<k{\leq}m$ of this operator does not belong to the domain $D_{\epsilon}$. We denote the boundary of domain $D_{\epsilon}$ by $\Gamma_{\epsilon}$. Without loss of generality we may assume that the points of spectrum $\lambda_{k}{\ne}0$ do not belong to $\Gamma_{\epsilon}$. Taking into account the equality $$(\Phi(0,x),g_{1}(x))=\lambda_{1}g_{1}(0),$$ we deduce from formulas (5.21) and (5.23) the relation $$p(t,\Delta)=
 \sum_{k=1}^{m}\sum_{j=0}^{n_{k}}e^{-t/\lambda_{k}}t^{j}c_{k,j}+J,$$ where $n_{k}$ is the index of the eigenvalue $\lambda_{k}$, $$J=-\frac{1}{2i\pi}\int_{\Gamma}\frac{1}{z}e^{-t/z}((B^{\star} -zI)^{-1}\Phi(0,x),1)dz.$$We note that $$n_{1}=1.$$ Indeed, if $n_{1}>1$ then there exists such a function 