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The paper deals with a new problem of physical correctness detection in the area of strictly causal system representations. The proposed approach to the problem solution is based on generalization of Tellegen's theorem well known from electrical engineering. Consequently, mathematically as well as physically correct results are obtained. The contribution is mainly concerned with presentation of a new structural approach to analysis and synthesis of linear and non-linear causal systems. It has been proven that complete analysis of instability, conservativity, dissipativity, anti-dissipativity, stability, asymptotic stability and chaoticity reduces to two independent tests: the monotonicity test of abstract state space energy and that of complete state observability, evtl. of its dual, i.e. complete state controllability property.