The Markushevich problem in the class of automorphic functions for arbitrary circle

In the article an explicit method for solution the Markushevich boundary value problem in the class of automorphic functions with respect of Fuchsian group $\Gamma$ of the second kind is suggested. The boundary condition of the problem is given on the main circle from which all limit points of the group are deleted. The the problem is found in closed form under additional restriction on the coefficients of the problem: the function $a(t)/(b(t)+1)$ is analytic in the domain $D_-$ and is automorphic with respect $\Gamma$ in this the domain.