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A significant mathematical error is identified and corrected in a recenthighly-cited paper on oscillatory flows of second-grade fluids [Fetecau &Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions areshown to agree identically with numerical ones generated by a finite-differencescheme, while the original ones of Fetecau & Fetecau do not. A list of otherrecent papers in the literature that commit the error corrected in this Commentis compiled. Finally, a summary of related erroneous papers in this journal ispresented as an Appendix.

Comments on: "Starting solutions for some unsteady unidirectional flows of a second grade fluid," [Int. J. Eng. Sci. 43 (2005) 781]