After having investigated the packings derived by horo-and hyperballs related to simple frustum Coxeter orthoscheme tilings, we consider the corresponding covering problems (briefly hyp-hor coverings) in n-dimensional hyperbolic spaces H n (n = 2, 3). In the 2− and 3−dimensional hyperbolic spaces we construct hyp-hor coverings generated by simply truncated Coxeter orthochemes, and we determine their thinnest covering configurations and their densities. We prove, that in the hyperbolic plane (n = 2) the density of the above thinnest hyp-hor covering arbitrarily approximates the universal lower bound of the hypercycle or horocycle covering density √ 12 π , and in H 3 the optimal configuration belongs to the {7, 3, 6} Coxeter tiling with density ≈ 1.27297, that is less than the previously known famous horosphere covering density 1.280 due to L. Fejes Tóth and K. Böröczky. Moreover, we study the hyp-hor coverings in truncated orthosche-mes {p, 3, 6} (6 < p < 7, p ∈ R), whose density function attains its minimum at parameter p ≈ 6.45962, with density ≈ 1.26885. That means, that this locally optimal hyp-hor configuration provide smaller covering density than the former determined ≈ 1.27297, but this hyp-hor packing configuration can not be extended to the entire hyperbolic space H 3 .