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It is studied the Hilbert boundary value problem for the nondegenerateBeltrami equations in domains $D$ of the complex plane $\mathbb C$ with theso--called quasihyperbolic boundary condition. It is proved the existence ofsolutions of this problem with coefficients of countably bounded variation andwith arbitrary boundary data that are measurable with respect to logarithmiccapacity. It is shown that the dimension of the spaces of such solutions isinfinite. It is also given applications to the Dirichlet, Neumann and Poincareboundary value problems for analogs of the Laplace equation in anisotropic andinhomogeneous media.

On Hilbert problem for Beltrami equations in quasihyperbolic domains