It is shown that an oscillatory character of the solutions of the collisionless kinetic equations describing production of the quark--gluon plasma in strong color fields leads to the exponential (thermal-like) transverse-momentum spectra of partons produced in the soft region (100  MeV < p_\perp < 1 GeV). In addition, the production of partons in the very soft region (p_\perp < 100 \hbox { MeV}) is clearly enhanced above the thermal-like background.

PACS numbers: 25.75.-q, 05.20.Dd, 24.85.+p