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Parity and time invariance violating forces produce collective P- and T- odd moments in nuclei with static octupole deformation. Collective Schiff moment, electric octupole and dipole and also magnetic quadrupole appear due to the mixing of rotational levels of opposite parity and can exceed single-particle moments by more than a factor of 100. This enhancement is due to two factors, the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. The above moments induce T- and P- odd effects in atoms and molecules. Experiments with such systems may improve substantially the limits on time reversal violation.