The goal of this paper is to develop a unified account of past and future tense morphology conveying irrealis in languages with no inflectional Mood. Unlike earlier works, the present approach draws a parallel between Tense and Mood themselves and not between particular realizations of these categories, such as past and irrealis. Extending Klein's (1995) and Demirdache & Uribe-Etxebarria's (2000) unified analysis of Tense and Aspect to Mood, the author proposes that Mood is a dyadic predicate that takes time-denoting phrases as arguments: Tense relates the utterance time T-Ut and the assertion time T-Ast, while Mood relates the evaluation time T-Evl and T-Ut. The examination of Russian and Hebrew shows that the analysis makes correct predictions regarding the relationship between Tense morphology and irrealis. Furthermore, it allows for a unified treatment of Tense, Aspect, and Mood—the three categories realized within the system of verbal inflection, which may shed new light on the grammatical expression of these categories cross-linguistically.