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This paper deals with steady-state and transient response of spheroidal antennas in a possible dispersive homogeneous isotropic environment. A modal approach has been used, properly modified in order to circumvent the divergence problem associated with the gap excitation. Conditions under which an input admittance can be unambiguously defined have been derived and an equivalent network given. Quite satisfactory comparisons with experiments and the King-Middleton second-order theory are indicated. The transient analysis has been performed with emphasis on three environmental situations (free space, conductive medium, plasma medium) shedding light on the physical mechanism of radiation in transient conditions.