A fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas is presented. The model has been verified for plasma beta (ratio of kinetic/magnetic pressures) in a range between 0.1 and 15. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes, Alfv¿nic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. Modes slower than the sound speed have left-handed polarization for the transverse magnetic field, while the faster modes have right-handed polarization. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits, it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas (¿ ≈ 1) and how trains of solitons (mirror modes) are produced in a hot, anisotropic plasma. The applicability of the model is illustrated by showing that the electric currents carried by nonlinear waves measured on Cluster spacecraft in the magnetosheath at ¿ ≈ 15 are well reproduced by currents derived from the theoretical model.