Angular distributions of protons from the 170, 174, 176Yb(t, p)172, 176, 178Yb and 178,180Hf(t, p)180, 182Hf reactions have been studied using beams of 15 MeV tritons from the McMaster University tandem Van de Graaff accelerator. The reaction products were analyzed with a magnetic spectrograph and detected with photographic emulsions. Levels up to ~2.5 MeV excitation were studied in each nuclide, with a typical overall resolution of ~15 keV (full-width half-maximum). Measurements were also made with targets of natural Yb and natural Hf, to improve the accuracy of relative strengths in each chain of isotopes, and with a target of 172Yb to facilitate the normalization of previously published data to the present results. One of the most notable features of the data is the large amount of L = 0 strength to excited Iπ = 0+ states for all cases where the residual nucleus has a neutron number N ≤ 108. The populations of these states are not explained by either the pairing rotational or vibrational models. The SU(3) limit of the interacting boson model yields qualitative but not quantitative agreement. For two of the residual nuclides studied, 178Yb and 182Hf, there was little or no nuclear structure information previously available. The (t, p) experiments have located a number of excited states in each of these cases, and also give the first measurements of two-neutron separation energies; S(n) = 12 333 ± 6 keV for 178Yb and 12 413 ± 6 keV for 182Hf.