The time-evolution of the wave packet inside chaotic and integrable two-dimensional nanostructures is numerically studied. Recently the time-evolution of quantum states is seriously considered to treat the dynamical property of nanostructures. By computer simulation, we have found the enhancement around the classical periodic orbits, which has been theoretically predicted. It is similar to the scars in the standing wave of the chaotic billiards and is also beyond the naive prediction of the random nodal patterns from the chaotic nanostructure. The initial position and velocity and the shape of the wave packet are crucial for the enhancement, however, we can observe that the remnant of the initial wave packet travels along the unstable periodic orbit. Then the wave packet gradually diffuses around the structure. This behavior has close relation to the dynamical properties of electrons in the structure, e.g., the conductivity, the magneto-resistance etc. Copyright (C) 2008 John Wiley & Sons, Ltd.