The quasienergy for the time-periodic Hamiltonian \p\(alpha) + v(theta
, t) on L-2[0,2 pi] has no absolutely continuous spectrum if 0 < alpha
< 1 and v(theta, t) is C-infinity, although the gap between successiv
e eigenvalues of \p\(alpha) is decreasing. (C) Elsevier, Paris.