Aims. A first-order asymptotic representation of higher-order non-radial g(+)-modes in spherically symmetric stars with a convective core is constructed from the full fourth-order system of governing equations. Stars are considered that, besides their convective core, also contain a radiative envelope, or both an intermediate radiative zone and a convective envelope. At the same time, the earlier asymptotic theory of Willems et al. (1997, A&A, 318, 99) relative to stars consisting of a convective core and a radiative envelope is made more transparent.