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The aim of the present work is to attempt to make a number of different glasses, based on tellurite as the principal former, which contain substantial quantities of zinc oxide up to 40 mol % ZnO. To study the longitudinal elastic properties, measurements have been made of the velocity of the longitudinal ultrasonic waves propagated through the prepared glasses. The results indicate that the longitudinal elastic constants depend strongly upon the composition of the prepared glasses. A detailed qualitative interpretation of the increase in the modulus is made. Information about the structure of the glass can be deduced after calculating the number of network bonds per unit volume and the crosslink density. The role of the halogen inside the glass network is discussed.