We review some recent investigations on the cumulative signal produced by extragalactic populations of gravitational wave sources at frequencies which might be interesting for LISA. In particular, we consider the contribution of extragalactic compact binary systems, accounting for the binaries which have been formed since the onset of galaxy formation in the Universe. The resulting gravitational signal appears to be largely dominated by close white dwarf binaries and represents a significant confusion 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 gravitational wave emission from the first stars, which are assumed to be very massive objects (VMOs) (Schneider et al 2000 Mon. 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 emitted during each collapse would be seen as a stochastic background. The predicted signal in a critical-density cold dark matter universe might be interesting for LISA. The expected emission rate is roughly 4000 events/yr, resulting in a stationary, discrete sequence of bursts, i.e. a shot-noise signal.