This paper deals with critical motion sequences, i.e. sequences of camera motions that lead to inherent ambiguities in uncalibrated Euclidean reconstruction or self-calibration. Concretely, we focus on how to deal with ambiguous reconstructions. We show that the ambiguous Euclidean reconstructions from a critical motion sequence are conjugated in a special sense. We discuss how these conjugacies may be used to identify all ambiguous Euclidean reconstructions, even if there are discrete solutions or disjoint families of solutions.