Joint work with Sophya Garashchuk (Universit of South Carolina). Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time evolution equations for the classical and nonclassical components of the momentum operator. The wavefunction normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.