The Ge-As-Se chalcogenide glasses is an interesting system to test the validity of different constraint models proposed for these materials, in view of the fact that this system has a wide glass forming range which makes it possible to measure composition dependent properties over ranges covering most predicted thresholds. We have measured the thermal parameters-thermal diffusivity, thermal effusivity, thermal conductivity and heat capacity-of Ge-As-Se glasses covering composition range in which thresholds in physical properties have been predicted for covalent glasses employing a modified photopyroelectric technique. Our results show that this system exhibits a minimum in heat capacity at an average coordination number Z = 2.4 corresponding to a 3-D network as per the Phillips-Thorpe model, whereas thermal conductivity exhibits a threshold maximum at Z = 2.67 which is in agreement with the Tanaka model. (C) 2003 Kluwer Academic Publishers.