We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds. Previously in [Br3] similar results were established for some domains on coverings of St...