Recursive definition of streams (infinite lists of values) have been proposed as a fundamental programming structure in various fields. A problem is to turn such expressive recursive definitions into an efficient imperative code for their evaluation. One of the main approach is to restrict the stream expressions to interpret them as a temporal sequence of values. Such sequential stream rely on a clock analysis to decide at what time a new stream value must be produced. In this paper we present a denotational semantics of recursively defined sequential streams. We show how an efficient implementation can be derived as guarded statements wrapped into a single imperative loop.