The paper investigates the longitudinal and transverse oscillations of an orbiting tether connecting a flexible platform and a subsatellite. The variation of tension along the tether due to the tether mass, as well as the effect of the platform equilibrium tilt on the tether tension are taken into account. The effects of tether to subsatellite mass ratio r, nondimensionalized offset a and platform equilibrium tilt ψo on the frequencies of elastic oscillations are examined. It is observed that the frequencies of longitudinal oscillations depend mainly on r, while those for the transverse oscillations can be expressed in the form λn2 = anr−1 + bn + Cnαψo, where λn is the nondimensionalized nth natural frequency, an, bn are constants, and cn varies linearly with r−1.

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