For several years, UNICORE and Globus have co-existed as approaches to exploiting what has become known as the ``Grid''. Both offer many services beneficial for creating and using production Grids. A cooperative approach, providing interoperability between Globus and UNICORE, would result in an advanced set of Grid services that gain strength from each other. This paper outlines some of these parallels and differences as they relate to the development of an interoperability layer between UNICORE and Globus. Given the increasing ubiquity of Globus, what emerges is the desire for a hybridised facility that utilises the UNICORE work-flow management of complex, multi-site tasks, but that can run on either UNICORE- or Globus-enabled resources. The technical challenge in achieving this, addressed in this paper, consists of mapping resource descriptions from both grid environments to an abstract format appropriate to work-flow preparation, and then the instantiation of work-flow tasks on the target systems. Other issues such as reconciling disparate security models and file transfer support are also addressed.