The laser beam transmission through a colloidal solution of CdSe/ZnS quantum dots in toluene is investigated for the case of a continuous sequence of femtosecond pulses (100 fs) at a frequency of 100 MHz and nanosecond pulses (15 ns) at a frequency of 10 kHz. It is found that a giant nonlinearity is photoinduced in the system. The magnitude of the photoinduced nonlinearity is determined from the number of rings in the interference structure of the intensity distribution in a distant zone of the beam transmitted through the cell. It is established that the induced nonlinearity of the colloidal solution of quantum dots depends linearly on the average power of laser beams. The time required to attain a stationary regime of the induced nonlinearity of the colloidal solution of quantum dots in toluene (i.e., the transient period) is determined and lies in the millisecond range. From analyzing the photoinduced nonlinearities measured under different excitation conditions, it is concluded that the observed nonlinearity exhibits a nonthermal nature. Possible physical mechanisms of the processes that can lead to long-lived induced nonlinearities in the medium are discussed. The general regularities are revealed in the processes responsible for the appearance of a giant nonlinearity of quantum dots in the toluene solution and the processes giving rise to blinking effects of quantum dots in organic matrices. The results of the investigations performed are of considerable interest for the development of nonlinear optical switches and nanophotonic devices based on composite nanomaterials.