A theoretical investigation of the (X) over tilde (2)A '' and (A) over tilde (2)A' electronic states of the HO2 radical is reported. Both electronic states have nonlinear equilibrium geometries and they correlate with a (2)Pi state at linear geometries so that they exhibit the Renner effect. In highly excited bending states, there is tunneling between two equivalent minima (with geometries where the H nucleus is bound to one, or the other, of the two O nuclei), and the two linear geometries H-O-O and O-O-H become accessible to the molecule. Thus, HO2 affords an example of the so-called double Renner effect. Three-dimensional potential energy surfaces for the (X) over tilde (2)A '' (A) over tilde (2)A' and electronic states of HO2 have been calculated ab initio and the global potential energy surfaces for the states have been constructed. These surfaces have been used, in conjunction with the computer program DR [Odaka et al., J. Mol. Structure 795, 14 (2006); Odaka et al., J. Chem. Phys. 126, 094301 (2007)], for calculating HO2 rovibronic energies in the "double-Renner"-degenerate electronic states (X) over tilde (2)A '' and (A) over tilde (2)A'. The results of the ab initio calculations, the rovibronic energies obtained, and analyses of the wavefunctions for selected states are presented. (c) 2008 American Institute of Physics.