Measurements of the magnetization, electrical resistance, ultrasonic attenuation and velocity, and the temperature variation resulting from flux jumps have been carried out on Nb-25%Zr in dc magnetic fields up to 100 kG. The values of the upper critical field Hc2 obtained from magnetization, resistance, and ultrasonic measurements are compared with each other. The temperature variation of Hc2 over the interval 1.5°K<=T<=Tc, where Tc=10.8°K, was determined from resistance measurements and the data are compared with the predictions of Maki's theory. It is found that the effects of the Pauli spin paramagnetism on the magnitude and temperature variation of the bulk upper critical field are smaller than those calculated from the theory of Maki. The effects of a magnetic field on the ultrasonic velocity and attenuation in the mixed and normal states of Nb-25%Zr are explained on the basis of the phenomenological theory of Alpher and Rubin. This theory accounts quantitatively for: (1) the attenuation edge of shear and longitudinal waves at Hc2, (2) the abrupt change in the velocity of shear waves at Hc2, and (3) the effect of a magnetic field on the attenuation of longitudinal and shear waves in the normal state. The Alpher-Rubin theory, although originally derived for impure metals in the normal state, also gives a good description of the behavior of ultrasonic waves in the megacycle range propagating in the mixed state if the electrical conductivity is taken to be infinite. At higher ultrasonic frequencies, however, deviations from the theory appear in the mixed state. If these deviations are to be explained within the framework of the Alpher-Rubin theory, one must postulate the existence of a finite effective ac resistance, in the mixed state, which is operative at these high frequencies. The data suggest that this ac resistance arises from viscous motion of the flux lines and that it is closely akin to the dc flow resistance. Observations of heating spikes and abrupt changes in the ultrasonic attenuation, which occur in one-to-one correspondence with flux jumps, are reported. Two of the salient features of the observed flux jumps, and the concomitant heating spikes, are their repetitive occurrence at fixed intervals of the magnetic field and the decrease in their relative spacing when the temperature of the sample is lowered. These features are discussed in light of the recent theory of Swartz and Bean for magnetic instabilities in the mixed state of high-field superconductors.