  The Mars-Simon tensor (MST), which e.g. plays a crucial role to provide gauge
invariant characterizations of the Kerr-NUT-(A)(dS) family, satisfies a
Bianchi-like equation. In this paper we analyze this equation in close analogy
to the Bianchi equation, in particular it will be shown that the constraints
are preserved supposing that a generalized Buchdahl condition holds. This
permits the systematic construction of solutions to this equation in terms of a
well-posed Cauchy problem. A particular emphasis lies on the asymptotic Cauchy
problem, where data are prescribed on a spacelike scri (i.e. for $\Lambda >0$).
In contrast to the Bianchi equation, the MST equation is of Fuchsian type at
scri, for which existence and uniqueness results are derived.
