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The first-order Raman spectra of the mixed-crystal layered compound HfxTi1-xSe2 have been studied over the whole range of concentrations 0≤x≤1. Both pure compounds, TiSe2 and HfSe2, have the CdI2 structure and so have two Raman-active phonons of A1g phonon is at about 205 cm -1. As x is decreased from 1.0, a new Raman peak, of A1g symmetry, appears near 180 cm -1. As x is decreased further, this peak shifts smoothly upwards in frequency, until it finally merges (by x=0.05) with the pure TiSe2 A1g phonon. A modified random-element isodisplacement model involving only short-range forces is developed to describe the observed concentration dependences of the frequencies of these phonons. The calculated concentration dependences are in good quantitative agreement with the experimental results.