In this thesis we investigated two systems of metallic glasses, binary NiZr and ternary CuHfTi. The binary NiZr system had been produced at the Faculty of Science in Sarajevo and it was investigated for its homogeneity, chemical composition, structure, thermal stability and microhardness, while Cu_55Hf_45-xTi_x (x=0, 5, ..., 45) system had already been examined by the same methods. Samples of both systems were examined by measurement of the heat capacity (C_p) in temperature range from 2 K to room temperature. Low temperature C_p parameters were determined and their relationship with glass forming ability (GFA) was checked. C_p of amorphous materials at sufficiently low temperature deviates from the Debye T^3 law with two major anomalies: almost linear contribution to the C_p below 1 K and a wide peak approximately at 10 K called boson peak (BP). Boson peak (BP) can be defined as an excess of low energy vibrational density of states compared to phonon contribution. A BP has been attributed to the localized vibrations, vibrations of medium range structures, localized defects, hybridization with localized vibrations. . . . On the other hand, BP has been attributed to Van Hove singularities in low-lying transverse acoustic phonon branch which produce similar excess contribution in crystalline materials. A BP was not observed in Ni_23Zr_77. The sample Ni_23Zr_77 was heated at different heating rates in order to detect the glass transition temperature and determine the fragility parameter. The obtained results are unusual, but we offer an appropriate microscopic explanation. The free volume can be reduced and therefore eliminate BP what can be achieved by slow cooling during the production process. In Ni_23Zr_77 the estimated cooling rate (h) is quite high, barely lower than typical h for melt spinning. We can tentatively suggest that the cooling rate close to h_c ~10^4 K/s is responsible for lack of BP. The results of our analysis show that in CuHfTi metallic glasses C_p parameters, position and amplitude of the BP exhibit monotonous dependence on the Ti content while the amplitude of BP scales with the amplitude of Debye contribution what may indicate that BP in this system is related to Van Hove singularity equivalent in glasses. Finally, it may be concluded that BP in metallic glasses of early and late transition metals does not reflect the glass forming ability of the alloys.