This workaddresses the problem of continuous query processing over infinite data streams. The paper defines new semantics for continuous queries and describes a continuous query processing system based on the concepts of continuous computations and online algorithms. A new programming control structure called as Continuous Iterator is proposed for implementation of continuous computations. The paper describes the semantics of three types of Continuous Iterators (composition, merge, and elimination), compares the iterators with the traditional relational algebra operations and proposes implementation of the iterators. The results of preliminary experiments are provided as well.