  We demonstrate both classically and quantum mechanically that the
Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is
nothing else, but oscillations of velocity assuring the energy conservation
when the electron moves in a periodic potential. This means that the nature of
electron ZB in a solid is completely different from that of relativistic
electrons in a vacuum, as proposed by Schrodinger. Still, we show that the
two-band {\bf k.p} model of electronic band structure, formally similar to the
Dirac equation for electrons in a vacuum, gives a very good description of ZB
in solids. Our results indicate unambiguously that the trembling motion of
electrons in solids should be observable.
