The reaction 70Ge(t,p)72Ge has been investigated with a 15-MeV triton beam. 30 levels of 72Ge were observed up to about 4-MeV excitation, four of which were unreported previously. Angular distributions were measured and compared with distorted-wave Born-approximation calculations. Several new 0+ states have been observed in 72Ge, one of which, at 1.709 MeV, is a new state and is the third 0+ level in 72Ge. Many additional spin and parity assignments have been made. The 72Ge nucleus shows a pattern of 0+ states that is considerable different from that of other even Ge isotopes. But for higher spins and both parities, 72Ge is very similar to other even Ge nuclei. NUCLEAR REACTIONS 70Ge(t,p), Et=15.0 MeV; measured σ(Ep,θ)72Ge deduced levels, L, π, J. DWBA analysis.