The article is devoted to the semantic analysis of Greek and Byzantine jokes, based on the language game with the temporal aspect of reality. Non-classical means of modal and temporal logic systems are applied in the article to the analysis of humor. The proposed logical models are not an exhaustive explanation of the fullness of funny aspects in a particular joke, but they represent the formal analogue of comic situations and comic techniques involving our understanding of time. The purpose of the article is to construct the tempo-modal joke models of the comic situations that assume our ability to relate the different modal and temporal axiomatic systems. In this regard, it would be possible to speak about “modal jokes”, “Russell jokes” and a “temporal jokes”.