- Two assumptions, one-dimensionality and quasineutrality, in the framework of the two-fluid hydrodynamics for hot plasmas, allow a close set of three equations (for inverse density and two components of the transverse magnetic field) to be obtained. These equations describe nonlinear waves in a wide range of wave vectors (up to the inverse electron inertial length) and frequencies (up to the low-hybrid frequency or in some cases electron gyrofrequency). The obtained set of equations is valid for arbitrary plasma temperatures. Linear dispersion relations are easily recovered from the obtained nonlinear equations. Nonlinear wave equations for different modes, which include new terms due to finite pressure, are derived using methods of the reductive perturbation theory. Stationary solutions are analyzed by the pseudopotential method. Conditions for the existence of solutions with homogeneous asymptotics are found.