This paper argues for a two-level theory of semantics as opposed to a one-level theory, based on the example of the system of temporal and durationM connectives. Instead of identifying the semantics of lexical items and larger constituents with conceptual structures, the two-level theory assumes that there is an intra-linguistic abstract semantic representations distinct from the extra-linguisticlevel of conceptual representations. It is argued that the two-level theory can give a more appropriate treatment of polysemy as well as a better account of the conditions under which connectives may (more or less) be felicitouslycombined with complement expressions which do not respect tileaspectual requirements of the connectives. 1 Semantic Representations and Conceptual Representations This paper addresses a specific question in the theory of natural language semantics with the example of a specific lexical domain. The question is whether one should opt for a one-level or a two-level theor...