Inelastic neutron scattering on solid 130XeF2 and 136XeF2 targets was utilized to populate excited levels in 130Xe and 136Xe. When calculating nuclear matrix elements vital to the understanding of double-beta decay, it is important to have a clear understanding of the low-lying level structure of both the parent and daughter nucleus. Of particular relevance to double-beta decay searches are the assignments of 0+ states. We show here that in the case of 130Xe there are several discrepancies in the adopted level structure. We found that one previous 0+ candidate level (1590 keV) can be ruled out and assigned two additional candidates (2223 and 2242 keV). In 136Xe we question the previous assignment of a 0+ level at 2582 keV. Excitation function and angular distribution measurements were utilized to make spin and parity assignments of levels and place new transitions. Owned by the authors, published by EDP Sciences, 2015.