This thesis deals with electrohydrodynamic convection in a horizontal fluid layer with temperature gradient. A simplified set of partial differential equations governing the motions of slightly conducting fluid is derived, taking into account the electric field effects. For small electric forces, convection is set in as a static mode. As the electric force becomes larger, convection occurs as a time-periodic motion. Transition from a static mode to an overstable mode takes place at a point determined by the Prandtl number. Nonlinear evolution of disturbances in quasicriticalstates is analyzed through the amplitude equations. Special attention is paid to ranges of parameters falling in the neighborhood of the degenerate bifurcation point. For a certain range of the Prandtl numbers, the hysteresis between the static mode and the overstable mode can appear. Subcritical instabilities are also possible for small or high enough values of the Prandtl number. Direct numerical simulation of the governing partial differential equations is also carried out. By the combination of Fourier-Chebyshev spectral method in space and finite difference method in time, the problem is reduced to a system of algebraic equations. Subcritical instabilities are confirmed for a small Prandtl number. The pattern of convection is steady for small electric forces. Two types of convective motion are possible when the imposed electric force gets larger. Transition between a steady branch and an oscillatory branch can occur either smoothly or abruptly according to the magnitude of the imposed electric field. The phenomenon of hysteresis is accompanied if the transition is accomplished by a jump, irrespectively of the Prandtl number.
