The piezoelectric ultrasonic composite oscillator technique (PUCOT) was used at frequencies near 120 kHz to measure the elastic and anelastic properties of two kinds of advanced ceramics as a function of temperature (T) up to about 1300 K and of strain amplitude in the range 10-7 to 10-4. The specimens consisted of commercially available silicon carbide (SiC) from Norton Co., reaction-formed SiC (RFSC) [with and without molybdenum disilicide (MoSi2) additions] made at NASA Lewis Research Center, and MoSi2/Ti5Si3 [With Ti5Si3 (pentatitanium trisilicide) concentrations in the range 10 to 50%] made at Los Alamos National Laboratory. The measured values of dynamic Young's modulus, E, damping, Q-1 and strain amplitude were analyzed. The main findings are: The Values of (1/E(0))(dE/dT), where E(0) is the value of E at room temperature, fall near -3 X 10-4 K-1; the damping in the materials is small and independent of strain amplitude for most of the specimens and temperatures used; and limited data for the silicides with 30 and 40% Ti5Si3 indicate a breakaway of the strain amplitude dependence of damping. The similarities and differences in the behavior of the mechanical properties are discussed for the two types of material.