Dynamical localization in general two-sided kicked rotors, which are classically nonintegrable, is shown to occur in the immediate vicinity of quantum antiresonance (periodic recurrences). A complete and exact solution of the quasienergy eigenvalue problem is obtained for the standard potential. Numerical evidence is given that this solution is an excellent approximation to the quantum dynamics and quasienergy states even not very close to antiresonance. The dynamical problem is mapped into a tight-binding model of a two-channel strip with pseudorandom disorder. One then has strong evidence for Anderson localization in this model near antiresonance.