We present observational data for two hydrogen-rich superluminous supernovae (SLSNe), namely SN 2013hx and PS15br. These objects, together with SN 2008es are the only SLSNe showing a distinct, broad H$\alpha$ feature during the photospheric phase and also do not show any clear sign of interaction between fast moving ejecta and circumstellar shells in their early spectra. Therefore we classify them as SLSN II as distinct from the known class of SLSN IIn. Both transients show a slow decline at later times, and monitoring of SN 2013hx out to 300 days after explosion indicates that the luminosity in this later phase does have a contribution from interaction. We detect strong, multi-component H$\alpha$ emission at 240 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 some bright type II (or type IIL) supernovae, although they have much higher luminosity and evolve on slower timescales. This comparison is qualitatively similar to how SLSN Ic compare with normal Ic. We applied two semi-analytical codes to fit the light curves of our two objects and SN 2008es. These are based on a diffusion model with energy input from a spinning down magnetar and the interaction between the ejecta and a dense uniform shell of H-rich material. Both scenarios can produce quantitative fits to the light-curves but they both have weaknesses. The overall observational data set would tend to favour the magnetar, or central engine, model as the source of the peak luminosity although the clear signature of interaction shown at 240 days past maximum indicates that interaction can play a role in the luminosity evolution of superluminous type II SNe at some phases.
