It is well known that the aktionsart/lexical aspect of a predicate influences the temporal interpretation and the aspectual marking of a sentence, and also that languages differ with respect to which aktionsart properties feed into the tense-aspect system (see e.g. Bohnemeyer & Swift 2004). In this paper, I try to pin down the exact locus of variation between languages where the stative–dynamic distinction is mainly grammaticized (e.g. English, Saamáka) and languages where the telic–atelic distinction is mainly grammaticized (e.g. Swedish, Chinese and Russian). The focus will be on the differences between English and Swedish, and I will argue that these two languages crucially differ in the nature of Assertion Time (or Topic/Reference Time, Klein 1994, Demirdache & Uribe-Etxebarria 2000): whereas the assertion time in English is always punctual in imperfective contexts, assertion time in Swedish can extend to include minimal stages of events. The Assertion Time is introduced by a (viewpoint) aspect head that is present in both languages, but not phonologically realized. The difference can thus not be ascribed to the presence or absence of overt tense, aspect or verb morphology, or to a special tense value, as argued in one way or other by, for example, Giorgi & Pianesi (1997), Demirdache & Uribe-Etxebarria (2000) and Ramchand (2012). Once this factor (i.e. the nature of Assertion Time) has been isolated, it becomes evident that all verbs in English and Swedish, regardless of telicity or dynamicity, can be assigned either a perfective or an imperfective value. Moreover, I will argue that the English progressive–non-progressive (or ‘simple’) distinction is independent of viewpoint aspect (i.e. the perfective– imperfective distinction) made in, for example, the Romance languages.