  We study the global boundedness of bilinear and multilinear Fourier integral
operators on Banach and quasi-Banach $L^p$ spaces, where the amplitudes of the
operators are smooth or rough in the spatial variables. The results are
obtained by proving suitable global boundedness of rough linear Fourier
integral operators with amplitudes that behave as $L^{p}$ functions in the
spatial variables. The bilinear and multilinear boundedness estimates are
proven by using either an iteration procedure or decomposition of the
amplitudes, and thereafter applying our global results for linear Fourier
integral operators with rough amplitudes.
