Spectral observations of the Sun in the vacuum-ultraviolet wavelength range by SUMER on SOHO led to the discovery of unusual emission features - called humps here - at 116.70 nm and 117.05 nm on either side of the He I 58.43 nm line. This resonance line is seen in the second order of diffraction, whereas the humps are recorded in the first order with the SUMER spectrometer. In its spectra both orders are superimposed. Two less pronounced humps can be detected at 117.27 nm and near 117.85 nm. After rejecting various possibilities of an instrumental cause of the humps, they are studied in different solar regions. Most of the measurements, in particular those related to the limb-brightening characteristics, indicate that the humps are not part of the background continuum. An assembly of spectrally-unresolved atomic or ionic emission lines might be contributing to the hump at 117.05 nm, but no such lines are known near 116.7 nm. It is concluded that we detect genuine radiation, the generation of which is not understood. A two-photon emission process, parametric frequency down conversion, and molecular emissions are briefly considered as causes of the humps, but a final conclusion could not be reached.