HfO2-Y2O3 and La2Zr2O7 are candidate thermal/environmental barrier coating materials for gas turbine ceramic matrix composite (CMC) combustor liner applications because of their relatively low thermal conductivity and high temperature capability. In this paper, thermal conductivity and high temperature phase stability of plasma-sprayed coatings and/or hot-pressed HfO2-5mol%Y2O3, HfO2-15mol%Y2O3 and La2Zr2O7 were evaluated at temperatures up to 1700 C using a steady-state laser heat-flux technique. Sintering behavior of the plasma-sprayed coatings was determined by monitoring the thermal conductivity increases during a 20-hour test period at various temperatures. Durability and failure mechanisms of the HfO2-Y2O3 and La2Zr2O7 coatings on mullite/SiC Hexoloy or CMC substrates were investigated at 1650 C under thermal gradient cyclic conditions. Coating design and testing issues for the 1650 C thermal/environmental barrier coating applications will also be discussed.