  This paper is devoted to the study of the analytic properties of Mahler
systems at 0. We give an effective characterisation of Mahler systems that are
regular singular at 0, that is, systems which are equivalent to constant ones.
Similar characterisations already exist for differential and (q-)difference
systems but they do not apply in the Mahler case. This work fill in the gap by
giving an algorithm which decides whether or not a Mahler system is regular
singular at 0.
