Innovation in the fields of wireless data communications, mobile devices and biosensor technology enables the development of new types of monitoring systems that provide people with assistance anywhere and at any time. In this paper we present an architecture useful to build those kind of systems that monitor data streams generated by biological sensors attached to mobile users. We pay special attention to three aspects related to the system efficiency: selection of the optimal granularity, that is, the selection of the size of the input data stream package that has to be acquired in order to start a new processing cycle; the possible use of compression techniques to store and send the acquired input data stream and; finally, the performance of a local analysis versus a remote one. Moreover, we introduce two particular real systems to illustrate the suitability and applicability of our proposal: an anywhere and at any time monitoring system of heart arrhythmias and an apnea monitoring system.