We have studied the radioactive line emission expected from solar active regions after large flares, following the production of long-lived radioisotopes by nuclear interactions of flare-accelerated ions. This delayed X- and gamma-ray line emission can provide unique information on the accelerated particle composition and energy spectrum, as well as on mixing processes in the solar atmosphere. Total cross sections for the formation of the main radioisotopes by proton, super(3)He, and a-particle reactions are evaluated from available data combined with nuclear reaction theory. Thick-target radioisotope yields are provided in tabular form, which can be used to predict fluxes of all of the major delayed lines at any time after a gamma-ray flare. The brightest delayed line for days after the flare is found to be the 511 keV positron-electron annihilation line resulting from the decay of several b super(+) radioisotopes. After 62 days however, the flux of the e super(+)-e super(-) annihilation line can become lower than that of the 846.8 keV line from the decay of super(56)Co into super(56)Fe. Our study has revealed other delayed gamma-ray lines that appear to be promising for detection, e.g., at 1434 keV from the radioactivity of both the isomer super(52)Mn super(m) (T sub(%) = 21.1 minutes) and the ground state super(52)Mn super(g) (T sub(%) = 5.59 days), 1332 and 1792 keV from super(60)Cu (T sub(%) = 23.7 minutes), and 931.1 keV from super(55)Co (T sub(%) = 17.5 hr). The strongest delayed X-ray line is found to be the Co Ka at 6.92 keV, which is produced from both the decay of the isomer super(58)Co super(m) (T sub(%) = 9.04 hr) by the conversion of a K-shell electron and the decay of super(57)Ni (T sub(%) = 35.6 hr) by orbital electron capture. Prospects for observation of these lines with RHESSI or future space instruments are discussed.