The asymptotic-energy limit of the density P ( S ) of spacings between adjacent levels of the two-dimensional harmonic oscillator ( T D H O ) spectrum is studied. It is shown that in any integer segment [ M , M + 11, containing -h f / a levels, of the TDHO spectrum m + an, P ( S ) has the form 1 w , S ( S -S,) where i takes on at most three values. For large M , P ( S ) displays strong level repulsion for irrational a, but it does not settle on a stationary form nor does its average over M . This is in marked contrast with the behaviour of generic integrable systems for which the Poisson statistics, P ( S ) = exp(-S), is known to apply.
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