This paper introduces a new family of Generic and Progressive algorithms (GPAC, for short) for continuous mobile queries over mobile objects. GPAC provides a general skeleton that can be tuned through a set of methods to behave as various continuous queries (e.g., continuous range queries and continuous k-nearest-neighbor queries). GPAC algorithms aim to provide three goals: (1) Online evaluation through an in-memory processing of the incoming mobile data. (2) Progressive evaluation through employing an incremental evaluation paradigm. (3) Fast query response through employing an anticipation paradigm. Query answer is anticipated and is cached in memory to allow for fast evaluation. GPAC algorithms are encapsulated in physical pipelined query operators. GPAC pipelined operators can be combined with traditional query operators in a query execution plan to support a wide variety of continuous queries. Experimental results based on a real implementation inside a prototype streaming database engine show the efficiency of GPAC operators in providing incremental and fast response for continuous queries.