We present a comprehensive study of the one-dimensional modulation instability of partially spatially incoherent light in noninstantaneous self-focusing media. For this instability to occur, the nonlinearity has to exceed a specific threshold that depends on the coherence properties of the beam. Above this threshold a uniform-intensity partially spatially coherent wave front becomes unstable and breaks up into periodic trains of one-dimensional stripes. © 2002 Optical Society of America.