- Two types of intermittency of passive scalar fluctuations (the intermittency in the systems with and without external pumping) are analyzed. We have shown that in the systems without external pumping under certain conditions there is a self-excitation of fluctuations of passive scalar (number density of particles advected by turbulent flow), and higher moments grow faster than lower moments. This can result in intermittency, i.e., the appearance of sharp peaks in which the main part of the field intensity is concentrated. We have also shown that in the systems with external pumping the anomalous scalings appear already in the second moment of passive scalar field when the degree of compressibility (i.e., the ratio of the energies in compressible and incompressible component of the velocity) is more than 1 / 27 . The mechanism for both, the small-scale instability and the anomalous scalings is associated with the compressibility of fluid flow or with the inertia of particles which results in a divergent velocity field of particles.