Two systems have been studied La2-xYxZr2O7 and La2-xYxHf2O7, as part of an on-going study of radiation tolerance in nuclear waste forms and related oxide materials. The structural effects of increasing Y content in La based zirconate and hafnate pyrochlores have been studied with neutron diffraction and electron microscopy. Results have shown a difference in structural stability for both the pyrochlore and fluorite phases within each system, including the presence of two-phase regions in both systems. In the zirconate, the two-phase region lies in the range x = 0.9-1.6. This is shifted to higher Y content in the hafnate system and lies in the range of x = 1.5 to approximately 1.8-1.9. In addition to the differences in phase stability, electron diffraction, predominantly down the  zone axis, has shown evidence for ordering in the form of structured diffuse scattering within the fluorite phases.