The magnetization reversal processes of single-layer nanoscale elliptical ring arrays are examined. The magnetic field was applied parallel or perpendicular to the long axis. The magnetization hysteresis loops showed a simultaneous-reversal single-step transition or two-step transition involving flux closure vortex states. For various aspect ratios and thicknesses, the transition between single-step and double-step magnetization reversals was measured to form phase diagrams. Simulations of the magnetization reversal behavior agreed with our results.