The soft optical phonons associated with the tetragonal-to-orthorhombic structural phase transition in La/sub 2-//sub x/Sr/sub x/CuO/sub 4-//sub y/ have been investigated using inelastic-neutron-scattering techniques. Single crystals with Sr concentration of x = 0, 0.08, and 0.14 were studied. Both branches of the doubly degenerate X-point phonon which go soft at the tetragonal-to-orthorhombic transition have been observed in the orthorhombic phase. In all three samples one branch hardens, while the other remains relatively soft with behavior indicative of a further incipient structural phase transition. We identify the hard and soft branches of the orthorhombic phase as zone center and zone-boundary phonons, respectively. The zone-center mode has A/sub g/ symmetry and is, consequently, Raman active. The relation of these measurements to other structural properties and to the superconductivity in La/sub 2-//sub x/Sr/sub x/CuO/sub 4-//sub y/ is discussed.