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A major challenge in RNA structure analysis is to infer common catalytic or regulatory functions based on primary sequences and secondary structures. Some programs have been developed that compare RNAs with such given structures. Nevertheless, the most important problem is that it is hard to determine the adopted structures of RNAs which are a necessary prerequisite to numerous applications; once a structure has been assigned to a sequence (e.g. the minimum free energy structure), it influences the output of the programs and thus affects the scientific result, especially when dealing with a set of multiple RNAs. In this paper, we go one step further and analyze distances between RNA structure ensembles. They reflect structural relationships computed basically on base-pairing probability matrices. We propose a distance measure between two base-pairing probability matrices showing similar or non-similar structural folding behaviour. This includes the detection of shared optimal, suboptimal and local secondary structures. Consequently, our distance measure avoids falling into the trap of fixing specific structures. A pairwise comparison strategy in a set of multiple RNAs leads us to construct a network of structural relationships using the neighbour joining method. Attempts to predict phylogenetic trees are discussed and demonstrated by means of viral RNAs.