This paper addresses nonclairvoyant and nonpreemptive online job scheduling in Grids. In the applied basic model, the Grid system consists of a large number of identical processors that are divided into several machines. Jobs are independent, they have a fixed degree of parallelism, and they are submitted over time. Further, a job can only be executed on the processors belonging to the same machine. It is our goal to minimize the total makespan. We show that the performance of Garey and Graham’s list scheduling algorithm is significantly worse in Grids than in multiprocessors. Then we present a Grid scheduling algorithm that guarantees a competitive factor of 5. This algorithm can be implemented using a “job stealing” approach and may be well suited to serve as a starting point for Grid scheduling algorithms in real systems.