The present paper seeks to propose a general framework to composite Web services selection. The proposed framework extends the conventional Web services architecture by adding a new component in the registry devoted to multicriteria classification of compositions into different ordered Quality of Service (QoS) classes. This additional component takes as input the specification of the desired service, a set of functional and non-functional evaluation criteria, a set of QoS-ordered classes, and a set of preference parameters, and generates as output a classification of composite Web services into different QoS-ordered classes. In addition to the description of the proposed framework, the paper proposes solutions to construct, evaluate and classify compositeWeb services. The paper also briefly presents the developed prototype and then illustrates and discusses some computational aspects of the proposed framework using numerical data.