The admittance characteristics of a system consisting of two centre-fed dipole antennas of arbitrary orientation are investigated. Each antenna is modelled by a very thin prolate spheroid which is centrally fed by a gap voltage. By using the equivalence principle, each spheroidal dipole is replaced by a solid spheroidal conductor of the same size without a gap, encircled by a corresponding filamentary ring carrying magnetic current of proper magnitude. The associated electric and magnetic fields are expanded in terms of appropriate vector spheroidal eigenfunctions and the boundary conditions at the surface of each spheroid are imposed by using the rotational-translational addition theorems for vector spheroidal wave functions. The solution of the resulting set of algebraic equations gives the unknown scattered field expansion coefficients. Numerical results are presented for the mutual admittance of two centre-fed thin spheroidal dipole antennas of arbitrary orientation, for various centre displacements. In addition, theEandHplane patterns are computed for the system of two dipole antennas in various configurations, with one dipole being parasitic.