The present paper reports a numerical investigation of natural convection and the associated mode-transition and hysteresis phenomena in a two-dimensional differentially heated inclined enclosure. Unsteady Navier-Stokes/Boussinesq equations governing the fluid flow and heat transfer are solved numerically. Rayleigh numbers in steady flow regime, 1 x 10(3) less than or equal to Ra less than or equal to 2 x 10(4), and the angles of inclination of 0 degrees less than or equal to gamma less than or equal to 90 degrees are considered in the computations. Major concerns are the effects of inclination on flow-mode transition. Enclosures of length-to-height aspect ratio As = 4, 3 and 1 are studied. Air of PI = 0.71 in an enclosure of As = 4 is chosen as the flow model to examine the influences of the inclination at various Rayleigh numbers. Hysteresis phenomena for Ra greater than or equal to 2000 are demonstrated. Parameter maps of Ra vs gamma for As = 4 with gamma increasing and decreasing are proposed, in which flow regimes characterized by various modes are designated. Effects of initial condition on the flow pattern formation are examined for As = 3. In a model of square enclosure (As = 1), effect of the imperfect thermal boundary conditions is examined to investigate the possible causes for inconsistency of the predictions with the experiments. The present study provides more physical insight into the natural convection in enclosures.