This work addresses the problem of maintaining the consistency of the answers to continuous queries which are posed by the users of the Moving Objects Databases (MOD). We propose a framework which enables detecting and processing the pending queries whose answers need to be re-evaluated upon modificatins to the MOD. Relevant syntactic elements of the user's queries and their semantic implications are identified, and the basic components of a system that can be used for this task are specified. We show how triggers can be used to maintain the answers to the users' queries "up to date" with respect to the modifications to the MOD and we demonstrate that our system can be implemented on top of the existing ORDBMS.