Ess-under-ess sentences, where the so-called past tense marker -ess in the complement clause of propositional attitude verbs occurs under -ess in the matrix clause, can be interpreted differently in some contexts. To take account of the semantic difference between the ess-under-ess sentences, I argue in this paper that the semantic contrast is due to types of predicates associated with -ess. After pointing out some problems with the previous treatments of -ess, I claim that -ess shows duality in the sense that it is parallel to the past tense in some contexts and to the present perfect in other contexts. As a way of disambiguating --ess, this paper comes up with certain types of predicates. That is, the exact meaning of -ess in a given context is dependent upon the types of predicates it is combined with. The predicate types, together with the duality of -ess, bring out semantically different interpretations of ess-under-ess sentences.