Calculations of the densities of states of amorphous Zr_cT_1-c alloys where T=Fe, Co, Ni or Cu, are presented. The method of calculation is an adaptation of the method used by the authors to analyse the virtual bound states on impurities in Ag and Cu alloys (1985). The values of the calculated densities of states at the Fermi level are used to draw conclusions concerning the magnetic susceptibilities chi and the specific heat coefficients gamma which are discussed as a function of Zr concentration, c. Agreement with some experimental trends is obtained and, in particular, a decrease in chi of gamma with increasing c in Zr_cCo_1-c and Zr_cFe_1-c alloys can be understood. This behaviour is attributed to the close proximity of the Co or Fe d band to the Zr d band.