This paper motivates the blend of social computing with service-oriented computing, giving "birth" to social Web services. On the one hand, social computing builds user applications upon the principles of collective action and content sharing. On the other hand, service-oriented computing builds enterprise applications upon the principles of service offer and demand and loose coupling. Thanks to this blend social Web services can operate taking into account with whom they worked in the past and with whom they would like to work in the future. To engineer social Web services, this paper presents a four-step method that addresses several questions related to the engineering exercise. These questions are what relationships exist between Web services, what social networks correspond to these relationships, how to build social networks of Web services, and what social behaviors can Web services exhibit. Experiences dealing with implementing social Web services are, also, reported in the paper. © 2011 IFIP International Federation for Information Processing.