The structure of decoupled positive-parity and semidecoupled negative-parity bands up to high spin in Hg197,199 has been studied using multinucleon transfer reactions with the Gammasphere array. A positive-parity band in Hg199 with the (νi13/2)3 decoupled configuration that deexcites to levels in the negative-parity sequences is newly established. The semidecoupled sequences in both isotopes are extended to higher spin. Rotation-aligned angular momenta and crossing frequencies determined from experiment are in fair agreement with those from cranking calculations. A transition from oblate collective rotation at low spin to triaxial noncollective shapes at high spin is indicated
