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The model of Preparata et al.  is used for system diagnosis. The problem of characterizing systems which are sequentially diagnosable is considered. A new concept (detection set), which gives a new insight to the structure of these systems, is defined in this paper and utilized to prove two theorems which expand the class of known sequentially diagnosable systems. An algorithm for finding a faulty unit is discussed, and a conjecture is stated which, if true, characterizes those systems. Finally, detection sets are also used in the context of Friedman's model of t/s diagnosability, to extend the repair strategies proposed by Karunanithi and Friedman  for single loop systems to systems whose diagnostic graph is strongly connected.