A theoretical investigation of the X(2)A" and A(2)A' electronic states of the HO(2) 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, HO(2) affords an example of the so-called double Renner effect. Three-dimensional potential energy surfaces for the X(2)A" and A(2)A' electronic states of HO(2) 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 HO(2) rovibronic energies in the "double-Renner"-degenerate electronic states X(2)A" and A(2)A'. The results of the ab initio calculations, the rovibronic energies obtained, and analyses of the wavefunctions for selected states are presented.