Lifetimes of excited states in Y99,Y101,Nb101,Nb103, and Nb105 were measured in an experiment using the recoil distance Doppler shift method at GANIL (Grand Accélérateur National d'Ions Lourds). The neutron-rich nuclei were produced in fission reactions between a U238 beam and a Be9 target. Prompt γ rays were measured with the EXOGAM array and correlated with fission fragments that were identified in mass and atomic number with the VAMOS++ spectrometer. The measured lifetimes, together with branching ratios, provide B(M1) and B(E2) values for the strongly coupled rotational bands built on the [422]5/2+ ground state in the Y and Nb nuclei with neutron number N≥60. The comparison of the experimental results with triaxial particle-rotor calcul...