Supervising secure communications for security and law enforcement considerations is intrinsically required for improving management issues with respect to the authorized relationships between supervisors and their subordinators in a security clearance hierarchy. That is, the contents of secure communications between any two communicating users can be supervised (or eavesdropped) by their corresponding supervisor(s). Consider the situation that the users with their security clearance hierarchy are formed as a tree, and it is assumed that only two users with the same immediate supervisor and have the same security clearance in the hierarchy can communicate secretly with each other. With the use of one-way hash functions, this talk presents two mechanisms, one is based on hardware approach and the other is based on software approach, to resolve hierarchically supervising secure communications stated above. Two communicating users can quickly obtain a shared session key by using the proposed mechanisms. Furthermore, this session key can be easily derived by the corresponding supervisor(s) of the communicating users, and hence the supervising requirements for the span of control can be achieved.