How might the basic compatibility of theory and observations be tested for nonlinear dynamic processes without imposing arbitrary stochastic restrictions on the process state variables? The present paper proposes a "flexible least cost" approach. For each possible estimated state sequence x, let CD (x) and cm(x) denote the costs incurred for deviations away from the prior dynamic and measurement specifications, respectively. The greatest lower bound for the set of cost vectors (cD(x), cm(x)) associated with all possible estimated state sequences x gives the locus oT minimal attainable dynamic and measurement costs. The estimated state sequences which attain the "cost-efficiency frontier" indicate the possible ways the actual process could have developed over time in a manner minimally incompatible with the prior dynamic and measurement specifications. An algorithm is developed for the exact sequential updating of the least-cost state estimates as the duration of the process increases and additional observations are obtained.