The description of resonances originating from several coupled electronic states in a diabatic or approximate diabatic basis can offer both:conceptual insights and computational challenges. In a three-state problem, two bound electronic states strongly coupled to a single dissociative continuum, large resonance energy shifts (thousands of cm(-1)), and Linewidths varying over 4 orders of magnitude can be encountered. In this work a nonperturbative computational approach is developed to treat this class of resonances. Expressions for both the radiative and radiationless decay rates are developed. Although the approach is nonperturbative, the linewidth is expressed in a Golden-Rule-type formula. The resonance energy is obtained from the iterative solution of an eigenvalue problem in the bound state space. These attributes enable efficient determination both narrow and broad linewidths and large resonance energy shifts. The approach is used to characterize both radiative and radiationless decay of the 2,3 (IIg)-I-3 states of Al-2, using a rigorous three-state diabatic basis. Lifetimes ranging from tenths of picoseconds to nanoseconds are determined. The corresponding resonance energy shifts are on the order of 4000 cm(-1).