  A general continuum-RPA approach is developed to describe electromagnetic
transitions between giant resonances. Using a diagrammatic representation for
the three-point Green's function, an expression for the transition amplitude is
derived which allows one to incorporate effects of mixing of single and double
giant resonances as well as to take the entire basis of particle-hole states
into consideration. The radiative widths for E1 transition between the
charge-exchange spin-dipole giant resonance and Gamow-Teller states are
calculated for ^{90}Nb and ^{208}Bi nuclei. The importance of the mixing is
stressed.
