Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the "not later than" relationship. In this paper, we first introduce the novel concept of generalized comtraces, extensions of comtraces that can additionally model the "non-simultaneously" relationship. We then study some basic algebraic properties and canonical forms of both comtraces and generalized comtraces. Finally we analyze in detail the relationship between (generalized) comtraces and (generalized) stratified order structures. The major technical contributions of this paper are the results showing that generalized comtraces and generalized stratified order structures can uniquely represent one another.
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