It is determined, during monitoring of a patient, that a plurality of alarm conditions has been initiated. The alarm conditions characterize a measurement by and/or operation of at least one medical device and have an associated grade among a plurality of prioritized grades. Thereafter, alarms can be generated that corresponding to some or all of the plurality of alarm conditions such that among concurrent active alarms: (i) an alarm corresponding to an alarm condition having a highest priority grade is conveyed at a first level upon initiation and, if such alarm condition remains active for a pre-defined time period, at the first level upon expiration of the pre-defined time period, and (ii) alarms corresponding to alarm conditions having equal or lower priority grades than the priority grade of the current highest priority grade alarm condition are conveyed at a second level, the second level being different from the first level.