The nearest neighbour level spacing distribution and the Delta(3) statistic of level fluctuations associated with very high spin states (I greater than or similar to 30) in rare-earth deformed nuclei are analysed by means of a cranked shell model, The many particle-many hole configurations created in the rotating Nilsson potential are mixed by the surface-delta two-body residual interaction, The levels in the near-yrast region show a Poisson-like level spacing distribution. As the intrinsic excitation energy U increases, the level statistics shows a gradual transition from order to chaos, reaching at U greater than or similar to 2 MeV the Wigner distribution typical of the Gaussian orthogonal ensemble of random matrices, This transition is caused by the residual two-body interaction, On the other hand, the level spacings between the yrast and the first excited state show a peculiar behaviour, displaying a Wigner-like distribution instead of the Poisson-like distribution seen for the other near-yrast rotational states, The lowest spacings reflect the properties of the single-particle orbits in the mean-field, and are only weakly affected by the residual two-body interaction. (C) 1997 Elsevier Science B.V.