Instruction Balanced Time Slicing (IBTS) allows multiple parallel jobs to be scheduled in a manner akin to the well-known gang scheduling scheme in parallel computers. IBTS however allows for time slices to change dynamically and, under dynamically changing workload conditions is a good non-clairvoyant scheduling technique when the parallel computer is time sliced one job at a time. IBTS-parallel is proposed here as a dynamic scheduling paradigm which improves on IBTS by allowing also dynamically changing space sharing of the computer’s processors. IBTS-parallel is also non-clairvoyant and it is characterized under the competitive ratio metric. A lower bound on its performance is also derived. Supported in part by the Irvine Research Unit in Advanced Computing and NASA under grant #NAG5-3692. Professor Alain Greiner is gratefully acknowledged. Supported by Capes, Brazilian Government, grant number 1897/95-11.