The photophysical properties of squaric acid derivatives bearing, two piperidino (SQ-DP) or two indolinylidenemethyl groups (SQ-IN) are determined and compared to the results of ab initio quaritum chemical calculations on smaller model systems. In both cases, a temperature-dependent nonradiative decay process is observed which quenches the fluorescence. The latter is especially efficient for SQ-DP, because the radiative transition is forbidden in this case. It is concluded that in both compounds, twisting relaxations are important, leading to a close approach of ground and excited states. For SQ-IN, this relaxation process is connected with an increase of the excited-state dipole moment and explains why the nonradiative losses are enhanced in polar solvents.