A thin current sheet with thickness comparable to the thermal ion gyroradius possesses free energy capable of driving a number of plasma instabilities for its destabilization. Among these instabilities is the drift-kink instability (DKI) unveiled through previous numerical simulations. To advance our theoretical understanding of DKI, we formulate a two-fluid theory with finite ion and electron temperatures in a one-dimensional (Harris) current sheet to examine the linear properties of DKI. We reduce the stability analysis to solving a nonlocal eigenvalue equation. We find that the eigenvalue equation gives a number of growing modes with both symmetric and antisymmetric magnetic perturbations with respect to the neutral sheet. These solutions have high growth rates, generally of the same order as their real frequencies, which are sizable fractions of the ion gyrofrequencies evaluated outside the current sheet. Near the center of the current sheet, the eigenfunction exhibits fine spatial structures with dimensions much smaller than the ion inertial length. These structures become progressively broadened as the ion to electron mass ratio is arbitrarily reduced. This theoretical result is potentially useful in assessing the impact of adopting unrealistic ion to electron mass ratio in numerical simulations of DKI or thin current sheet stability. ¿ 1998 American Geophysical Union