Summary: We show that the one-dimensional self-organizing Kohonen algorithm (with zero or two neighbours and constant step \(\varepsilon)\) is a Doeblin recurrent Markov chain provided that the stimuli distribution \(\mu\) is lower bounded by the Lebesgue measure on some open set. Some properties of the invariant probability measure \(\nu^ \varepsilon\) (support, absolute continuity, etc.) are established as well as its asymptotic behaviour as \(\varepsilon \downarrow 0\) and its robustness with respect to \(\mu\).