A testable processor system (10,20) comprises a plurality of modules (11,12,...In). Each module (11) comprises a processor unit (110) and a debug controller (111). The debug controllers are coupled to a common test access point controller (TAP- controller 20), and have a test data input (Tin), a test data output (Tout) and at least one test register (112, 113). The test data inputs and outputs of the debug controllers (111, 121, 131, ...,InI) are arranged in a scan chain having an input for receiving test input data (TDI) from the TAP-controller and an output for providing test output data (TDO) to the TAP-controller. At least one debug controller (111) has a selection facility (115) to select whether data in the scanchain is either shifted through the at least one test register (112) of that debug controller (111) or is immediately forwarded from the test data input (Tin) to the test data output (Tout) of that debug controller. The at least one debug controller has a bypass register (117) which controls the selection facility. The TAP-controller (20) provides a control signal (BYPASS CNTRL) which, when active, selects the bypass register as part of the scan chain.