  We have developed the mean-field theory of coexisting charge-density waves
(CDW) and unconventional charge-density waves (UCDW). The double phase
transition manifests itself in the thermodynamic quantities and in the magnetic
response, such as spin susceptibility and spin-lattice relaxation rate. Our
theory applies to quasi-one dimensional (TaSe_4)_2I, where above the CDW
transition, thermal fluctuations die out rapidly, but robust pseudogap
behaviour is still detected. We argue, that the fluctuations are suppressed due
to UCDW, which partially gaps the Fermi surface, and causes non-Fermi-liquid
(pseudogap) behaviour.
