One-dimensional wave equation for two electrons in nanoring whose height and width are much smaller than the diameter is derived. The energies of the two-electron low-lying states arising from the two-electron rotation around the axis and their dependencies on the nanoring diameter, height and width are analysed. The level-ordering and crossovers of the corresponding curves related to the strong electron-electron interaction are studied and discussed. In the limit case as the height and width of the ring tend to zero our results coincide with those obtained previously for a one-dimensional nanoring. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)