  Electronic structure calculations, using the charge and spin self-consistent
Korringa- Kohn-Rostoker (KKR) method, have been performed for several $R$Mn$X$
compounds ($R$ = Mg, Ca, Sr, Ba, Y; $X$ = Si, Ge) of the CeFeSi-type structure.
The origin of their magnetic properties has been investigated emphasizing the
role of the Mn sublattice. The significant influence of the Mn-Mn and Mn-$X$
interatomic distances on the Mn magnetic moment value is delineated from our
computations, supporting many neutron diffraction data. We show that the marked
change of $\mu_{Mn}$ with the Mn-Mn and Mn-$X$ distances resulted from a
redistribution between spin-up and spin-down $d$-Mn DOS rather than from
different fillings of the Mn 3$d$-shell. Bearing in mind that the neutron
diffraction data reported for the $R$Mn$X$ compounds are rather scattered, the
KKR computations of $\mu_{Mn}$ are in fair agreement with the experimental
values. Comparing density of states near $E_{F}$ obtained in different magnetic
orderings, one can notice that the entitled $R$Mn$X$ systems seem to 'adapt'
their magnetic structures to minimize the DOS in the vicinity of the Fermi
level. Noteworthy, the SrMnGe antiferromagnet exhibits a pseudo-gap behaviour
at $E_{F}$, suggesting anomalous electron transport properties. In addition,
the F-AF transition occurring in the disordered La$_{1-x}$Y$_{x}$MnSi alloy for
the $0.8<x<1$ range is well supported by the DOS features of
La$_{0.2}$Y$_{0.8}$MnSi. In contrast to the investigated $R$Mn$X$ compounds,
YFeSi was found to be non-magnetic, which is in excellent agreement with the
experimental data.
