The new FLYA automated resonance assignment algorithm determines NMR chemical shift assignments on the basis of peak lists from any combination of multidimensional through-bond or through-space NMR experiments for proteins. Backbone and side-chain assignments can be determined. All experimental data are used simultaneously, thereby exploiting optimally the redundancy present in the input peak lists and circumventing potential pitfalls of assignment strategies in which results obtained in a given step remain fixed input data for subsequent steps. Instead of prescribing a specific assignment strategy, the FLYA resonance assignment algorithm requires only experimental peak lists and the primary structure of the protein, from which the peaks expected in a given spectrum can be generated by applying a set of rules, defined in a straightforward way by specifying through-bond or through-space magnetization transfer pathways. The algorithm determines the resonance assignment by finding an optimal mapping between the set of expected peaks that are assigned by definition but have unknown positions and the set of measured peaks in the input peak lists that are initially unassigned but have a known position in the spectrum. Using peak lists obtained by purely automated peak picking from the experimental spectra of three proteins, FLYA assigned correctly 96-99% of the backbone and 90-91% of all resonances that could be assigned manually. Systematic studies quantified the impact of various factors on the assignment accuracy, namely the extent of missing real peaks and the amount of additional artifact peaks in the input peak lists, as well as the accuracy of the peak positions. Comparing the resonance assignments from FLYA with those obtained from two other existing algorithms showed that using identical experimental input data these other algorithms yielded significantly (40-142%) more erroneous assignments than FLYA. The FLYA resonance assignment algorithm thus has the reliability and flexibility to replace most manual and semi-automatic assignment procedures for NMR studies of proteins.