Abstract We present two hydrogen-rich superluminous supernovae (SLSNe): SN2103hx and PS15br. These objects, together with SN2008es, are the only SLSNe showing a distinct, broad H α feature during the photospheric phase; also, they show no sign of strong interaction between fast moving ejecta and circumstellar shells in their early spectra. Despite the fact that the peak luminosity of PS15br is fainter than that of the other two objects, the spectrophotometric evolution is similar to SN2103hx and different from any other supernova in a similar luminosity space. We group all of them as SLSNe II and hence they are distinct from the known class of SLSN IIn. Both transients show a strong, multicomponent H α emission after 200 d past maximum, which we interpret as an indication of the 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 time-scales. 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 code to fit the light curves of our two objects and SN2008es. 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 late-time interaction indicates that interaction can play a role in the luminosity evolution of SLSNe II at some phases.