The Single European Electronic Market (SEEM) is expected to stimulate the take-up of eBusiness in Europe, increasing the competitiveness of SMEs through advanced eBusiness process models and tools, by offering to companies a model for modernizing work organization that allows them to face changing markets with an effective use of Information and Communication Technologies (ICT). However, the Building and Construction industry (B&C) has its ICT fragmented, having in the Building Information Model (BIM) paradigm a vehicle to address this problem. Interfacing with BIM brings another layer of complexity, mostly due to the heterogeneity of the systems and applications that need to interface with it. Thus, the adoption of a cluster of proper services in the Web that can offer in a unique way the functionalities needed for the adoption of BIM, is essential. The implementation of BIM under the Cloud Computing paradigm holds the promise of accelerating the B&C industry to achieve the Single Electronic Market. After presenting the vision for a Single European Electronic Market, and the expectation of the B&C sector to be integrated in a universal information space, this paper proposes the SOA4BIM framework as a cloud of services that enables universal access to the BIM paradigm by any system, application, or end user on the web.