/ AbstractWe present two hydrogen-rich superluminous supernovae (SLSNe), namely SN2013hx and PS15br. These objects, together with SN2008es are the only SLSNe showing a distinct, broad Halpha feature during the photospheric phase and also do not show any sign of strong interaction between fast-moving ejecta and circumstellar shells in their early spectra. Despite PS15br peak luminosity is fainter than the other two objects, the spectrophotometric evolution is similar to SN2013hx and different than any other supernova in a similar luminosity space. We group all of them as SLSNe II and hence distinct from the known class of SLSN IIn. Both transients show a strong, multi-component Halpha emission after 200 days past maximum which we interpret as an indication of interaction of the ejecta with an asymmetric, clumpy circumstellar material. The spectra and photometric evolution of the two objects are similar to type II supernovae, although they have much higher luminosity and evolve on slower timescales. This is qualitatively similar to how SLSNe I compare with normal type Ic in that the former are brighter and evolve more slowly. We apply a magnetar and an interaction semi-analytical codes to fit the light curves of our two objects and SN2008es. The overall observational dataset would tend to favour the magnetar, or central engine, model as the source of the peak luminosity although the clear signature of late-time interaction indicates that interaction can play a role in the luminosity evolution of SLSNe II at some phases.