  We establish the complete spectral exponential, and the strong
Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle
Anderson tight-binding model and for weakly interacting particles system. In
other words, we show stability of the one-dimensional localization from the
single-particle to multi-particle systems with an arbitrary large but finite
number of particles and for sufficient weakly interacting models. The proof
uses the multi-scale analysis estimates for multi-particle systems. The common
probability distribution function of the random external potential in the
Anderson model is assumed to be log-H\"older continuous, so the results apply
to a large class of Anderson models.
