Dynamic subgrid models of the eddy-viscosity, mixed and Clark types are tested on two compressible time-developing mixing layers. The first layer has a free-stream temperature ratio of 1 and a convective Mach number of 1.2. The second layer has a temperature ratio of 3 and a Mach number of 0.88. The dynamic Clark model is extended to model the energy convective subgrid terms. The models are evaluated using DNS data. A-priori analysis shows the best predictions by the dynamic mixed and Clark models. A posteriori analysis shows inconsistency for a LES formulation that uses the Fourier method in the homogeneous directions and a 6th order Pade scheme in the transverse direction. Implementing the 3/2-zero-padding rule for the convective resolved parts and a 4th order Pade scheme for the subgrid modelling removes that inconsistency for all models, where the dynamic Clark model also requires filtering its gradient part by a low-pass filter. A moderate transverse grid-stretching enables to reduce the number of points by half. For the current LES formulation, the dynamic mixed and Clark models are the most accurate for the cold and hot layers respectively. Modelling the energy subgrid terms is found to improve the LES prediction of the thermal energy for the hot layer.