The Zr41Ti14Cu12.5Ni10Be22.5 alloy in short-range order (SRO) metallic glassy, medium-range order metallic glassy, crystallized, and equilibrium crystalline states was prepared. The low temperature specific heat C-p of the alloy in the different states has been investigated. The results show that the SRO glass has largest specific heat among the four states, and C-p decreases with the extent of crystallization or degree of structural ordering in the alloy. The densities of states at the Fermi level, N(E-F), and Debye temperatures, theta(D), of the alloy are determined. It is found that N(E-F) for the SRO glass is highest among the four states, and it decreases with the structural ordering. The phenomenon is interpreted by localization of electrons in glassy alloys. The value of theta(D) increases with degree of structural ordering, indicative of marked soften transverse phonons in the SRO glass compared with the other states. (C) 2002 American Institute of Physics.