The dynamical processes underlying evolution over geological timescales remain unclear(1,2). Analyses of time series of the fossil record have highlighted the possible signature of periodicity in mass extinctions(3,4), perhaps owing to external influences such as meteorite impacts, More recently the fluctuations in the evolutionary record have been proposed to result from intrinsic nonlinear dynamics for which self-organized criticality provides an appropriate theoretical framework(5-7). A consequence of this controversial(8) conjecture is that the fluctuations should be self-similar, exhibiting scaling behaviour like that seen in other biological(9) and socioeconomic(10,11) systems. The self-similar character is described by a 1/f power spectrum P(f), which measures the contributions of each frequency f to the overall time series. If self-similarity is present, then P(f) approximate to f(-beta) with 0 < beta < 2, This idea has not been sufficiently tested, however, owing to a lack of adequate data, Here we explore the statistical fluctuation structure of several time series obtained from available palaeontological data bases, particularly the new ’Fossil Record 2’(18). We find that these data indeed show self-similar fluctuations characterized by a 1/f spectrum. These findings support the idea that a nonlinear response of the biosphere to perturbations provides the main mechanism for the distribution of extinction events.