  A kind of doubly special relativity theory proposed by J. Magueijo and L.
Smolin [Phys. Rev. Lett. 88, 190403 (2002)] is analysed. It is shown that this
theory leads to serious physical difficulties in interpretation of kinematical
quantities. Moreover, it is argued that statistical mechanics and
thermodynamics cannot be resonably formulate within the model proposed in the
mentioned paper.
