In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue-a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index &ggr; and a dimensionless quantity &kgr; the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and &ggr;. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for &ggr;>1 and all values of &kgr;, only oscillations are possible. For &ggr;1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of &kgr; and &ggr;, collapse may be averted. ¿ American Geophysical Union 1995