This paper presents a time-synchronous search concept in which (a) the language model contexts are represented in local hypotheses lists, as in N-best decoding, and where (b) these hypotheses lists are rescored using a language model in a time-delayed manner. The concept is shown to work well on a real 12000-word continuous-speech recognition task with a phonetic-tree based search. A faster though approximative search algorithm is presented which compares favorably well with the exact ones. - The discussion starts with some new aspects on word-dependent N-best decoding. Keywords: continuous speech recognition, search, N-best decoding, top N.