Abstract: The interpretation of past tense has long been a hot topic for logicians and semanticians.Single-index tense system, like Prior tense logic, as well as traditional scope analysis, is not adequate in interpreting the past tense in English compound sentences.Only by adopting multiple-index tense system, can these problems, especially that of "later-than-matrix" interpretation, be solved properly.The following are the properties of multiple-index tense system: (1) Predicates have an extra argument slot for a time; (2) Tense morphemes are time variables that saturate the time argument slots of predicates; (3) The meanings of anteriority and simultaneity derive from phonologically null elements that stand in a certain relation with tense morphemes; (4) The evaluation times are represented in the object language with a phonologically null time variable, represented as t^*.Multiple-index tense system can be used to disambiguate the meanings produced by the past tense morpheme in compound sentences, and to explain how ambiguity arises.