Evolution of sharp angular distributions in the degenerate two-dimensional gas of colliding electrons has been shown to occur essentially otherwise than in the three-dimensional gas. As early as after a few collisions the electron distribution function becomes antisymmetric in momentum, conserving, practically, its sharpness. Further spreading of this distribution in coordinate and momentum spaces occurs rather slowly, taking much more time than an electron-electron collision. Application of an extremely weak magnetic field leads to essential changes in this picture. The possibility of observing new effects in experiments on electron beam evolution in heterostructures is discussed.