This paper presents a process modeling language known as the GridPML for the composition of Grid Services. The GridPML is an XML-based language that supports basic control flow constructs adopted from Web Service composition languages with features for invoking Grid Services. The GridPML defines an approach to Grid Service lifecycle management that creates service instances as needed at run time. The GridPML also supports the use of process parameters, complex type variable assignment from different Grid Services, and collection type indexing. A process execution history containing the execution context is created and maintained by the GridPML execution engine, forming the basis of future research for analyzing the semantic correctness of concurrent process execution. In addition to presenting the design and implementation of the GridPML language, this paper also outlines future directions for exception handling and recovery features for the GridPML language and execution environment.