Abstract <p> A family of conservative difference schemes for calculating viscous gas flows in arbitraryorthogonal curvilinear coordinates is constructed on the basis of a Cartesian Godunov-typedifference scheme of the general type. The algorithms of the basic scheme for calculating thenumerical flows remain unchanged. It is shown that the schemes of the constructed family havethe second order of approximation in space, provided that the numerical flows of the basic schemeare calculated with a second or higher order of accuracy.</p>