In this work we deal with oblique derivative problems for elliptic equations. In the first part we formulate a geodetic boundary-value problem, where the domainis formed by a bounded space outside the Earth, while a boundary condition in the form of an oblique derivative is prescribed on Earth's surface and Dirichlet boundary condition is given on the other part of the boundary. Then we summarize the basic results about uniqueness of solution where we use strong maximum principle, as well the theory of existence result in Hölder spaces. Finally we presentconditions for existence result of geodetic boundary-value problem on special domain (spherical cap).