We show that a certain class of spatially partially coherent solitons, name
ly, twisted Gaussian Schell-model solitons, exists in a logarithmically sat
urable nonlinear medium with a noninstantaneous temporal response. Unlike p
reviously reported Gaussian Schell-model solitons, those discussed here car
ry a position-dependent twist phase, which vanishes in the fully coherent l
imit. We demonstrate that the presence of the twist phase provides an oppor
tunity for controlling the degree of spatial coherence of such solitons wit
hout affecting their intensity.