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Let $K/k$ be a finite Galois CM-extension of number fields whose Galois group$G$ is monomial and $S$ a finite set of places of $k$.\ Then the "Stickelbergerelement" $\theta_{K/k,S}$ is defined.\ Concerning this element,\ Andreas Nickelformulated the non-abelian Brumer and Brumer-Stark conjectures and their "weak"versions.\ In this paper,\ when $G$ is a monomial group,\ we prove that theweak non-abelian conjectures are reduced to the weak conjectures for abeliansubextensions.\ We write $D_{4p},\ Q_{2^{n+2}}$ and $A_4$ for the dihedralgroup of order $4p$ for any odd prime $p$,\ the generalized quaternion group oforder $2^{n+2}$ for any natural number $n$ and the alternating group on 4letters respectively.\ Suppose that $G$ is isomorphic to $D_{4p}$,\$Q_{2^{n+2}}$ or $A_4 \times \mathbb{Z}/2\mathbb{Z}$.\ Then we prove the$l$-parts of the weak non-abelian conjectures,\ where $l=2$ in the quaternioncase,\ and $l$ is an arbitrary prime which does not split in$\mathbb{Q}(\zeta_p)$ in the dihedral case and in $\mathbb{Q}(\zeta_3)$ in thealternating case.\ In particular,\ we do not exclude the 2-part of theconjectures and do not assume that $S$ contains all finite places which ramifyin $K/k$ in contrast with Nickel's formulation.\

On non-abelian Brumer and Brumer-Stark conjectures for monomial CM-extensions