  Assuming the Riemann hypothesis, we investigate the distribution of gaps
between the zeros of \xi'(s). We prove that a positive proportion of gaps are
less than 0.796 times the average spacing and, in the other direction, a
positive proportion of gaps are greater than 1.18 times the average spacing. We
also exhibit the existence of infinitely many normalized gaps smaller (larger)
than 0.7203 (1.5, respectively).
