The authors compare classical and quantum dynamics in the quasiclassical region of parameters and under the condition of unstable (chaotic) classical behavior. They estimate the characteristic time-scale at which classical and quantum solutions start to differ significantly. The method is based on exact equations for time-dependent expectation values in boson and spin coherent states, and applies to rather general Hamiltonians with many degrees of freedom. The authors develop a consistent dynamical theory for quantum nonintegrable Hamiltonians and provide explicit examples of classical-quantum "crossover-time", a very common and fundamental phenomenon in quantum nonintegrable systems. This book can be recommended to graduate students and to specialists.