It is currently stated and widely accepted by industry and users that the RAIM is designed to provide timely warnings in the situation where only one of the range measurements used at the current epoch is affected by an unacceptable bias. However, given the range of potential applications of RAIM in the future, in particular with the advent of Galileo and the generalization of Safety of Life applications, which should spread from the civil aviation community to many other professional sectors, it is very important to better understand the fundamental properties of RAIM, and in particular the potential of RAIM to detect multiple failures on range measurements. The purpose of the study presented in this paper is to analyze the performance of a RAIM in the presence of multiple simultaneous range errors. In particular, we conduct a theoretical analysis to determine in which cases the Least Squares Residuals RAIM detection criterion is not affected, and analyzed results of Monte-Carlo simulations in presence of up to four range failures. The theoretical analysis outlined above aims at determining in what conditions the Least Squares Residuals RAIM detection criterion remains unaffected by multiple range failures, searching for what we call criterion unaffecting range errors. We show that, provided the satellite constellation does not have any degenerated geometrical properties, the dimension of the vector sub-space of these criterion unaffecting errors is max(4-(N-p),0), where N is the number of tracked satellites and p is the number of faulty pseudorange measurements. The immediate conclusion is that if N-4 pseudo range measurements are affected, or less than that, by a large error, there exists no error that will not affect the RAIM detection criterion, and globally due to the negligible probability that unintentional interference lies in a small dimension sub-space, the RAIM detection criterion exhibits a natural detection capability even if up to N-2 pseudo-range measurements are faulty. This theoretical result defines the properties of the errors that lead to zero change in the detection criterion. To jump to a more operational conclusion, it remains to know what the possibility is for multiple range errors to induce a detection criterion that is below the detection threshold. So to complement the theoretical analysis outlined above, we ran Monte Carlo simulations inserting up to four range failures and analyzing the detection capacity. The capacity of RAIM detection is also analyzed in the presence of intentional jamming.