In order to lay a foundation for understanding kinetic effects on waves and instabilities in reversed field pinches, three different plasma models are employed to study linear perturbations of uniformly magnetized, infinite, homogeneous, current‐carrying plasmas. Two different types of instability emerge: configuration‐space instabilities driven by the macroscopic current and velocity‐space instabilities driven by the relative drift between electrons and ions parallel toB. The dispersion properties of waves and parallel current and drift‐driven instabilities with frequencies below the ion gyrofrequency are used to establish the physics limitations of the asymptotic guiding center plasma model. This model is then used to investigate parallel drift‐driven instabilities in fully self‐consistent, cylindrically symmetric, radially inhomogeneous equilibria that manifest large parallel currents and strong magnetic shear, as in reversed field pinches. The results of the cylindrical guiding center plasma are compared with those of the current‐carrying infinite plasma to illustrate the effects of the magnetic shear and curvature generated by the equilibrium current. Although quantitative differences appear, the same qualitative features are found in each case. The results illuminate the nature of current‐carrying plasmas. The dispersion properties of shear Alfve´n waves in such a plasma are very different from &ohgr;=k∥cA. Some of the modified shear Alfve´n waves that propagate against the current are destabilized by resonant electrons.