With the help of high-resolution long-slit and integral-field spectroscopy observations , the number of confirmed cases of galaxies with counterrotation is increasing rapidly . The evolution of such counterrotating galaxies remains far from being well understood . In this paper we study the dynamics of counterrotating collisionless stellar disks by means of N -body simulations . We show that , in the presence of counterrotation , an otherwise gravitationally stable disk can naturally generate bending waves accompanied by strong disk heating across the disk plane , that is in the vertical direction . Such conclusion is found to hold even for dynamically warm systems with typical values of the initial vertical-to-radial velocity dispersion ratio \sigma _ { z } / \sigma _ { R } \approx 0.5 , for which the role of pressure anisotropy should be unimportant . We note that , during evolution , the \sigma _ { z } / \sigma _ { R } ratio tends to rise up to values close to unity in the case of locally Jeans-stable disks , whereas in disks that are initially Jeans-unstable it may reach even higher values , especially in the innermost regions . This unusual behavior of the \sigma _ { z } / \sigma _ { R } ratio in galaxies with counterrotation appears not to have been noticed earlier . Our investigations of systems made of two counterrotating components with different mass-ratios suggest that even apparently normal disk galaxies ( i.e. , with a minor counterrotating component so as to escape detection in current observations ) might be subject to significant disk heating especially in the vertical direction .