In this note we compare two different mathematical hyperbolic models in dual-phase-lag heat conduction proposed by Tzou, and we ask for the parameter regions where stability can be expected. It is demonstrated that the parameter regions for the two lag-parameters T-q and To are different for the two models. That is, for certain parameters, in one model stability is expected while for the other one it is known that it is not stable. The first apparent contradiction is contrasted with the fact that known values for real materials (several metals are considered here) are in a range where both models predict stability or non-stability, respectively. Still, as a conclusion, one model should be considered only in a restricted parameter region. (c) 2005 Elsevier Ltd. All rights reserved.