Propagating exciton-polaritons at high density have been investigated by observing spatial evolution of their nonlinear optical response in typical layered crystals BiI3 and GaSe. In BiI3 characteristic excitons whose center-of-mass motion is confined at a quasi-two-dimensional space of a stacking fault interface (stacking fault excitons: SFEs) show more efficient spatial expansion for higher excitation densities. In order to detect an in-phase motion of the exciton-polaritons at high density, the degenerate four-wave-mixing (DFWM measurements with two laser beams were performed for both the crystals in a space-resolved regime. It turned out that the DFWM light is emitted from the polarization induced not only by the direct exciting laser light but also by coherently propagating exciton masses established separately by the other exciting laser light. This suggests a new type of collective motion of exciton-polaritons in a condensed phase. In GaSe the DFWM signal intensity exhibits k-vector dependence of the incident laser lights in the space-resolved regime. These results are discussed in terms of nonlinear polarization due to coherent collective motion of exciton-polaritons at high density. (C) 2000 Elsevier Science B.V. All rights reserved.