We review some recent investigations on the cumulative signal producedby extragalactic populations of gravitational wave sources at frequencieswhich might be interesting for LISA. In particular, we consider thecontribution of extragalactic compact binary systems, accounting for thebinaries which have been formed since the onset of galaxy formation inthe Universe. The resulting gravitational signal appears to be largelydominated by close white dwarf binaries and represents a significantconfusion noise component for LISA at frequencies between 1 and 10 mHz(Schneider et al 2001 Mon. Not. R. Astron. Soc. 324 797).Going further in the high redshift Universe, we consider the gravitationalwave emission from the first stars, which are assumed to be very massiveobjects (VMOs) (Schneider et al 2000Mon. Not. R. Astron. Soc. 317 385).If the final fate of VMOs is to collapse,leaving very massive black hole remnants,then the gravitational waves emittedduring each collapse would be seen as astochastic background. The predictedsignal in a critical-density cold darkmatter universe might be interesting forLISA. The expected emission rate isroughly 4000 events/yr, resulting in astationary, discrete sequence of bursts,i.e. a shot-noise signal.