In this paper, a hardware design of digital systems with remote-diagnostic capability is presented. We consider a method for testing a system T(l) on a module basis with a remotely installed systems T(2). In the testing mode, we set up a system (T(l)-m,m') such that a module m of T(l) is replaced by an adapter A(1) connected to other adapter A(2) through a telephone line and the corresponding module m' of T(2) is connected to A(2). If the system (T(l)-m,m') can simulate T(1) in the absence of any faluts, then it can test m' under a self test program. The main subject of this paper is to study the conditions of the system to be testable in the above sense. At first, the remote diagnostic network based on the system in this paper, restrictions to the system configuration required to perform such a diagnosis and the operation of the diagnostic system are described. The second, the module structure to make above simulation possible is considered, representing the system configuration graphically. Finally, an example of the adapter is shown and the time consumed to diagnose is discussed. One of our results is that a sufficiently large class of synchronous digital systems with few minor conventions is testable.