  For the weakly interacting one-dimensional multi-particle Anderson model in
the continuum space of configurations, we prove the spectral exponential and
the strong dynamical localization. The results require the interaction
amplitude to be sufficiently small. The general strategy uses the multi-scale
analysis bounds. Actually, we show that the multi-scale analysis bounds of the
single particle model remain stable when passing to multi-particle systems,
provided that the inter-particle interaction is sufficiently small. The common
probability distribution of the i.i.d. random external potential in the
Anderson model, is only needed to be log-H\"older continuous.
