Athwart immersions were introduced by F. J. Craveiro de Carvalho and S. A. Robertson [J. Aust. Math. Soc., Ser. A 37, 282-286 (1984; Zbl 0556.57024)] as a pair of immersed hypersurfaces with no tangent plane in common. In this paper this notion is generalized to immersed hypersurfaces of hyperbolic spaces. Using the Beltrami projection of hyperbolic space onto Euclidean space of the same dimension, it is shown that athwartness is preserved in both directions. This is used to transfer the results given in the Euclidean case [loc. cit.] to the hyperbolic case.