Abstract: Lifetimes of the 9/2(1)(-) and 3/2(1)(-) states in Co-63 and the 9/2(1)(-) state in Co-65 were measured using the recoil distance Doppler shift and the differential decay curve methods. The nuclei were populated by multinucleon transfer reactions in inverse kinematics. gamma rays were measured with the EXOGAM Ge array and the recoiling fragments were fully identified using the large-acceptance VAMOS spectrometer. The E2 transition probabilities from the 3/2(1)(-) and 9/2(1)(-) states to the 7/2(-) ground state could be extracted in Co-63 as well as an upper limit for the 9/2(1)(-) -> 7/2(1)(-) B(E2) value in Co-65. The experimental results were compared to large-scale shell-model calculations in the pf and pfg(9/2) model spaces, allowing us to draw conclusions on the single-particle or collective nature of the various states.