  Bonatti and da Luz have introduced the class of \emph{multi-singular
hyperbolic} vector fields to characterize systems whose periodic orbits and
singularities do not bifurcate under perturbation (called star vector fields).
  In this paper, we study the Sina\"{\i}-Ruelle-Bowen measures for
multi-singular hyperbolic vector fields: in a $C^1$ open and $C^1$ dense subset
of multi-singular hyperbolic vector fields, each {$C^\infty$} one admits
\emph{finitely} many physical measures whose basins cover a \emph{full}
Lebesgue measure subset of the manifold. Similar results are also obtained for
$C^1$ generic multi-singular hyperbolic vector fields.
