The near-maximum spectra of most superluminous supernovae that are not dominated by interaction with a H-rich CSM (SLSN-I) are characterised by a blue spectral peak and a series of absorption lines which have been identified as OII. SN2011kl, associated with the ultra-long gamma-ray burst GRB111209A, also had a blue peak but a featureless optical/UV spectrum. Radiation transport methods are used to show that the spectra (not including SN2007bi, which has a redder spectrum at peak, like ordinary SNe Ic) can be explained by a rather steep density distribution of the ejecta, whose composition appears to be typical of carbon-oxygen cores of massive stars which can have low metal content. If the photospheric velocity is ~10000-15000 km/s, several lines form in the UV. OII lines, however, arise from very highly excited lower levels, which require significant departures from Local Thermodynamic Equilibrium to be populated. These SLSNe are not thought to be powered primarily by 56Ni decay. An appealing scenario is that they are energised by X-rays from the shock driven by a magnetar wind into the SN ejecta. The apparent lack of evolution of line velocity with time that characterises SLSNe up to about maximum is another argument in favour of the magnetar scenario. The smooth UV continuum of SN2011kl requires higher ejecta velocities (~20000 km/s): line blanketing leads to an almost featureless spectrum. Helium is observed in some SLSNe after maximum. The high ionization near maximum implies that both He and H may be present but not observed at early times. The spectroscopic classification of SLSNe should probably reflect that of SNe Ib/c. Extensive time coverage is required for an accurate classification.
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