Anisotropic resistivity causes paramagnetic effects (Bz'(r)<0) in a screw pinch, being basically different to the self-relaxation in reversed field-pinches. The authors compute, analytically and numerically, the resulting influence on the plasma radius and on plasma beta in a straight cylindrical plasma. The results seem to indicate that D-D screw-pinch reactors which depend on safety factors q(a)>1 are unattainable. Diamagnetism caused by radial particle diffusion and the Nernst effect is also discussed. In a tokamak or reactor plasma, diamagnetism is shown to be negligible, whereas it may contribute in present ultra-low q, Extrap and RFP experiments. A basic relation is derived for the coupling between the poloidal and axial magnetic field components with the above effects included. Of specific importance to the Extrap programme is the result that plasma current limitation can arise due to the lack of equilibrium when the plasma radius tends to exceed its upper limit, which is defined by a magnetic or material limiter. Comparisons are made with stability limits depending on the safety factor, the number of contained ion Larmor radii and the line density.