Context : The hot subdwarf B star HS 0702+6043 is known as a large-amplitude , short-period p -mode pulsator of the EC~14026 type . Its atmospheric parameters place it at the common boundary between the empirical instability regions of the EC~14026 variables and the typically cooler long-period g -mode pulsators of the PG 1716 kind . Aims : We analyse and interpret the photometric variability of HS 0702+6043 in order to explore its asteroseismological potential . Methods : We report on rapid wide band CCD photometric observations to follow up on and confirm the serendipitous discovery of multiperiodic long-period luminosity variations with typical time scales of \sim 1 h in HS 0702+6043 , in addition to the two previously known pulsations at 363 s and 383 s. In particular , we isolate a relatively low-amplitude ( \sim 4 mmag ) , long-period ( 3538 \pm 130 s ) light variation . Results : We argue that the most likely origin for this luminosity variation is the presence of an excited g-mode pulsation . If confirmed , HS 0702+6043 would constitute a rare addition to the very select class of pulsating stars showing simultaneously parts of their pressure and gravity mode pulsation spectra . The asteroseismological potential of such stars is immense , and HS 0702+6043 thus becomes a target of choice for future investigations . While our discovery appears consistent with the location of HS 0702+6043 at the common boundary between the two families of pulsating sdB stars , it does challenge theory ’ s current description of stability and driving mechanisms in pulsating B subdwarfs . Conclusions :