Particle methods, also known as Sequential Monte Carlo methods, are a principled set of algorithms to approximate numerically the optimal lter in non-linear non-Gaussian state-space models. However, when performing maximum likelihood parameter inference in state-space models, it is also necessary to approximate the derivative of the optimal lter with respect to the parameter of the model. Poyiadjis et al. [2005, 2011] present an original particle method to apoproximate this derivative and it was shown in numerical examples to be numerically stable in the sense that it did not deteriorate over time. In this paper we theoretically substantiate this claim. Lp bounds and a central limit theorem for this particle approximation are presented. Under mixing conditions these Lp bounds and the asymptotic variance are uniformly bounded with respect to the time index.