Summary: The equivariant main conjecture of Iwasawa theory is shown to hold for a Galois extension $K/k$ of totally real number fields with Galois group an $l$-adic pro-$l$ Lie group of dimension 1 containing an abelian subgroup of index $l$, provided that Iwasawa's $\mu$-invariant $\mu(K/k)$ vanishes.
