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The backbone structure of a protein is largely determined by the ϕ and ψ torsion angles. Thus, knowing these angles, even if approximately, will be very useful for protein-structure prediction. However, in a previous work, a sequence-based, real-value prediction of ψ angle could only achieve a mean absolute error of 54° (83°, 35°, 33° for coil, strand, and helix residues, respectively) between predicted and actual angles. Moreover, a real-value prediction of ϕ angle is not yet available. This article employs a neural-network based approach to improve ψ prediction by taking advantage of angle periodicity and apply the new method to the prediction to ϕ angles. The 10-fold-cross-validated mean absolute error for the new method is 38° (58°, 33°, 22° for coil, strand, and helix, respectively) for ψ and 25° (35°, 22°, 16° for coil, strand, and helix, respectively) for ϕ. The accuracy of real-value prediction is comparable to or more accurate than the predictions based on multistate classification of the ϕ−ψ map. More accurate prediction of real-value angles will likely be useful for improving the accuracy of fold recognition and ab initio protein-structure prediction. The Real-SPINE 2.0 server is available on the website . Proteins 2008. © 2008 Wiley-Liss, Inc. [ABSTRACT FROM AUTHOR]