Quality of Service (QoS) is defined as a set of perceivable attributes expressed in a user-friendly language with parameters that may be subjective or objective. Objective parameters are those related to a particular service and are measurable and verifiable. Subjective parameters are those based on the opinions of the end-users. We believe that quality of service should become an integral part of multimedia database systems and users should be able to query by requiring a quality of service from the system. The specification and enforcement of QoS presents an interesting challenge in multimedia systems development. A deal of effort has been done on QoS specification and control at the system and the network levels, but less work has been done at the application/user level. In this paper, we propose a language, in the style of constraint database languages, for formal specification of QoS constraints. The satisfaction by the system of the user quality requirements can be viewed as a constraint satisfaction problem, and the negotiation can be viewed as constraints relaxation. We believe this paper represents a first step towards the development of a formal framework for quality of service management in video databases.