Nongyrotropic (gyrophase bunched) ion distributions in a magnetoplasma are studied by analytical methods and by two-dimensional hybrid code simulations. Nongyrotropy may not occur in a plasma being simultaneously homogeneous, stationary, and solenoidal in phase space. A detailed study is performed for a homogeneous and stationary plasma with sources and sinks in phase space. The analytical investigation cast in the framework of linearized Maxwell-Vlasov theory yields a coupling of low-frequency left-handed, right-handed, and longitudinal modes. Nongyrotropic ion distributions are unstable; they excite left-handed waves. The growth rate is comparable to that of the ion ring instability. The hybrid code simulation study confirms the expected propagation direction parallel to the background magnetic field. Three diffusion processes are studied: arc lengthening, arc broadening, and arc radius decreasing corresponding to particle energy diffusion. The characteristic diffusion time-scales are found to be of the order of 10¹ wave cycles.