A particle approximation of Feynman-Kac distributions is presented here, that combines SIS and SIR algorithms in the sense that only a part of the importance weights is used for resampling, and two different approaches are proposed to analyze its performance. The first approach is based on a representation in terms of path-space distributions, and could be used to analyze the joint particle approximation of distributions for a reference model and several alternate models at the same time. The second approach, which is of independent interest and seems very promising, is based on a representation in terms of a multiplicative functional, and could be used to analyze particle approximation with adaptive resampling schemes.