Management of alerts triggered by unexpected or hazardous changes in a patient's state is a key task in continuous monitoring of patients. Using domain knowledge enables us to specify more sophisticated triggering patterns for alerts, based on temporal patterns detected in a stream of patient data, which include both the temporal element and significant domain knowledge, such as "rapidly increasing fever" instead of monitoring of only raw vital signals, such as "temperature higher than 39 C". In the current study, we introduce iALARM, a two-tier computational architecture, accompanied by a language for specification of intelligent alerts, which represents an additional computational [meta] level above the temporal-abstraction level. Alerts in the iALARM language consist of (a) the target population part (Who is to be monitored?); (b) a declarative part (What is the triggering pattern?), i.e., a set of time and value constraints, specifying the triggering pattern to be computed by the bottom tier; and (c) a procedural part (How should we raise the alarm? How should we continue the monitoring and follow-up?), i.e., an action or a whole plan to apply when the alert is triggered, and a list of meta-properties of the alert and action. One of our underlying principles is to avoid alert fatigue as much as possible; for instance, one can specify that a certain alert should be activated only the first time that the triggering pattern is detected, or only if it has not been raised over the past hour. Thus, we introduce a complete life cycle for alerts. Finally, we discuss the implied requirements for the knowledgeacquisition tool and for the alert monitoring and procedural application engines to support the iALARM language. We intend to evaluate our architecture in several clinical domains, within a large project for remote patient monitoring.