The nuclides 98Mo and 100Mo have been studied in photon-scattering experiments by using bremsstrahlung produced from electron beams with kinetic energies from 3.2 to 3.8 MeV. Six electromagnetic dipole transitions in 98Mo and 19 in 100Mo were observed for the first time in the energy range from 2 to 4 MeV. A specific feature in the two nuclides is the de-excitation of one state with spin J = 1 to the 0+ ground state as well as to the first excited 0+ state, which cannot be explained in standard models. We present a model that allows us to deduce the mixing coefficients for the two 0+ shape-isomeric states from the experimental ratio of the transition strengths from the J = 1 state to the 0+ ground state and to the 0+ excited state.