Approximate analytical results are obtained for the propagation of an axisymmetric gravity current in a system rotating around a vertical axis, which occurs when a dense fluid intrudes horizontally under a lighter ambient fluid. Situations for which the density difference between the fluid is due either to compositional differences or to suspended particulate matter are considered; for the the latter, particle-driven cases, two models for the particle transport, turbulent remixing and laminar sedimentation are implemented. Attention is focused on situations in which the apparent importance of the Coriolis terms relative to the inertial terms, represented by the parameter C (the inverse of a Rossby number), is not large. A box-model approximation is used, in which the current is described as a control volume composed of a cylinder with a conical "roof＇ subject to global conservation conditions and simplifying assumptions. This leads to ordinary differential equations from which it is possible to calculate readily such essential features as the behaviour of the radius of propagation, height of the head (nose) and the amount of settled particles (when applicable). In particular, the limitation imposed by the Coriolis effects on the radius of propagation, the time of attainment of the maximal spread, and the appearance of an attached reverse motion are properly reflected. For the particle-driven case a parametric dependency between the settling and Coriolis influences is obtained, which allows for a stringent comparison to be made between the two different particle-transport models. The box model results are in good qualitative agreement with numerical solutions of the full shallow-water equations, for which a novel similarity transform is also presented.