A data processing system including multiple execution pipelines each having multiple execution stages E1, E2, E3 may have instructions issued together in parallel despite a data dependency therebetween if it is detected that the result operand value for the older instruction will be generated in an execution stage prior to an execution stage which requires that result operand value as an input operand value to the younger instruction and accordingly cross-forwarding of the operand value is possible between the execution pipelines to resolve the data dependency.