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The statistical properties of the energy levels calculated for the doubly-odd nuclei 84 y, 124Cs and 156Tb within the queasiparticle plus axially symmetric rotor model are studied by means of the two standard statistical tests of random-matrix theory, i.e. the distribution function p ( s) of the nearest-neighbour level spacings and the spectral rigidity (Δ3 statistics). We also investigate the Brody distribution function pB (s) with a single parameter that describes the chaotic degree of the systematic dynamics and the transition behaviour of the spectral fluctuations between Poisson and Gauss orthogonal ensemble limits.