A data processing system supports execution of both native instructions and Java bytecodes using a hardware executer for the Java bytecodes where possible and a software instruction interpreter for the Java bytecodes where these are not supported by the hardware. The sequences of native instructions 26 within the software instruction interpreter that perform the processing for the Java bytecodes being interpreted terminate within a sequence terminating instruction BXJ that acts differently depending upon whether or not an enabled hardware executer 6 is detected to be present. If an enabled hardware executer is detected as present, then the execution of the next Java bytecode is attempted with this. If an active hardware executer is not present, then the next Java bytecode is passed directly to the software instruction interpreter.