The crossover from conventional Fermi-liquid (FL) behavior to the Luttinger-liquid-like behavior in the two-dimensional single-band small-U Hubbard model near half filling is demonstrated. The applicability of the FL picture is discussed. This crossover is reproduced in the fermionic channel of the t-J model, if the fermion-fermion interaction is taken into account. The results are in qualitative agreement with the normal-state resistivity and photoemission data on the high-Tc cuprates.