On the number of quasimodes of whispering gallery type

New two-sealing expansion for eigenfunctions of whispering gallery type and corresponding eigenvalues of Laplace operator with Dirichlet and Heumaan boundary conditions in the plane region is offered. Eigen functions localize in a vicinity of the boundary and are enumerated by two natural numbers $(q, p)$ where $q$ and $p$ are respectivly numbers of knots along the boundary and along the normal to it. The validity of this asymptotic expansion is ensured provided $0\leqslant p\leqslant{\rm const}\:q^{1-\varepsilon}$ for $\forall\varepsilon\in(0, 1]$ where $q\to\infty$.