Nonlocal behavior is accommodated in the framework of thermal lagging to describe heat transport in phonon systems. In steady state the emphasis is on capturing the linear dependence of the effective thermal conductivity of thin nanowires on their radius. In ultrafast transient validation of the nonlocal/lagging model is furnished by its precise correlations with the thermomass model. A new type of thermal wave results from the first order nonlocality. Entering the second-order effects of nonlocality, special features include diminution of the sharp wavefront, a localized zone with a finite width, and much wider affected regions due to phonon scattering. (C) 2010 Elsevier Ltd. All rights reserved.