A kinetically complete measurement of the 12 C( 10 Be, α+α+n) and ( 10 Be, α+α) reactions has been performed at a beam energy of 30 MeV/nucleon. The charged beam velocity particles were detected in an array of Si-CsI detectors placed at zero degrees, and the neutrons in an 81-element neutron array. The coincident detection of the final-state particles, produced in the breakup of 10 Be, allowed the reconstruction of the excitation energy in the 8 Be and 9 Be systems. States in 8 Be were identified, in particular the ground and first-excited states; and in 9 Be, states at 1.68, 2.43, and (2.78, 3.05) MeV were observed. The population of these levels, in particular the 2.43 MeV 5/2 − level, suggests that collective excitations play an important role in the neutron removal process. Distorted wave Born approximation and Glauber-type calculations have been used to model the direct neutron removal from the 10 Be ground state and the two-step removal via inelastic excitations of the 10 Be(2 + ) and 9 Be(5/2 − ) excited states.