  We deal with mixed weak estimates of Fefferman-Stein type for higher order
commutators of Calder\'on-Zygmund operators with BMO symbol. The results
obtained are Fefferman-Stein inequalities that include the estimates proved in
\cite{BCP22(JMS)} for the case of singular integral operators, as well as the
classical weak endpoint estimate for commutators given in \cite{PP01}.
  We also consider commutators of operators involving less regular kernels
satisfying an $L^{\Phi}$--H\"ormander condition. Particularly, the obtained
results contain some previous estimates proved in \cite{BCP22(JMS)} and
\cite{Lorente-Martell-Perez-Riveros}.
