The structure of the nightside coma in the vicinity of a strongly active comet nucleus of pure ice is investigated by solving gasdynamic equations for the flow of water vapour sublimated from-or condensed onto-the nucleus surface. To guarantee the physical validity of the solution, both Euler and Navier-Stokes Equations are solved, and the solutions are compared. A spherical nucleus is considered first and then a triaxial ellipsoidal nucleus. The results show that (1) a fluid coma of significant extent and very complicated physical structure is formed; (2) for low heat conduction transfer across the nucleus from the dayside to the nightside surface, a narrow conical weak shock appears near to the antisolar axis: the whole nightside surface acts as a cold trap for the vapor, part of which recondenses onto it; (3) for intermediate heat conduction, part of the nightside surface becomes weakly sublimating, and a different weak shock pattern is formed; and (4) at high heat conduction, the whole nightside surface is weakly sublimating, and the resulting how pattern becomes similar to that existing in a coma formed by diffusion from the nucleus interior (see Crifo, Rodionov and Bockelee-Morvan, 1999, Icarus 138, 83-106). The results are compared to related model results by other authors, and a discussion is made of their relevance to the 1996 observation of the near-nucleus nightside coma of Comet C/1996 B2 Hyakutake. (C) 2000 Academic Press.