The chapter describes local thermal nonequilibrium (LTNE). At a microscopic level, the temperature and the rate of heat flux at the interface between solid and fluid phases must be identical, but the average temperature over a representative elementary volume( REV) does not have to yield identical temperatures for the two phases. Many papers exist which either derive or use equations that govern local thermal nonequilibrium phenomena in porous medium convection, where the intrinsic average of the temperatures of the solid and fluid phases may be regarded as being different. Most of the papers that deal with convective flows in porous media assume that LTE is valid, and it is therefore important to acquire some criteria that will indicate when this is not a good assumption. The chapter compiles and presents the most commonly used model equations. The chapter discusses some of the most recent research using these equations. The simplest of these model equations that are routinely solved for specific convective flows are described in the chapter. The chapter focuses primarily on free and forced convection boundary layers, and free convection within cavities.