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Using graph grammars as a formal tool that supports the distributed system description necessitates a solution to both the problem of assurance of cohesion distributed subgraphs describing the system and making possible cooperation of (different) graph grammars (that will modify these graphs). The definition of conjugated graph grammars, introduced in the paper, seems to be a possible solution of the above problem. Moreover, for some subclass of these grammars - the strictly conjugated graph grammar - it can be proven that consistency of conjugated graphs system will not be violated by productions of this kind of grammars. An example application SCG grammar limitation to the algebraic DPO approach is finally presented.