  The paper starts out from pseudomeasures (in the sense of Serre) which hold
the arithmetic properties of the abelian $l$-adic Artin $L$-functions over
totally real number fields. In order to generalize to non-abelian $l$-adic
$L$-functions, these abelian pseudomeasures must satisfy congruences which are
introduced but not yet known to be true. The relation to the ``equivariant main
conjecture'' of Iwasawa theory is discussed.
