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Optical absorption is calculated for asymmetric double quantum wells in intense terahertz (THz) fields applied parallel to the growth direction z. Owing to the lack of inversion symmetry, strong Coulombic coupling (CC) occurs between excitons. The effects of CC and various Stark effects due to the THz field-exciton interactions on the excitonic absorption are systematically studied. The absorption spectra show a rich variety of behaviors, including excitonic sidebands and replicas as well as peak splittings. Due to the optical Stark effect (OSE), Autler-Townes (AT) splittings occur in resonant THz fields whose frequency is near the transition frequency connecting two exciton energy levels, with the absorption of each exciton splitting into a double peak. Taking CC into account causes a pronounced asymmetry in the AT doublets as the oscillator strength is transferred from the higher-energy exciton to the lower of the pair. In a low-frequency driving THz field, multiple features emerge in the vicinity of the strong exciton peak, being separated from it by multiples of the THz-photon energy, nh Omega (n=+/- 1,+/- 2,+/- 3,...). The multiple features are the THz-photon sidebands and replicas of the exciton and arise from different band-to-band transitions. The occurrence of the sidebands and replicas is proved to be due to the second-order Stark effect (SOSE). Including CC, the excitonic absorption connected with weak band-to-band transitions can occur with a great strength, and the overall absorption is significantly enhanced for a wide range of THz frequencies. The features of the AT splittings, the excitonic sidebands and replicas, and their variation with the THz field are well explained in terms of the CC and the Stark effects (OSE and SOSE).