We prove weighted strong inequalities for the multilinear potential operator
${\cal T}_{\phi}$ and its commutator, where the kernel $\phi$ satisfies certain
growth condition. For these operators we also obtain Fefferman-Stein type
inequalities and Coifman type estimates. On the other hand we prove weighted
weak type inequalities for the multilinear maximal operator
$\mathcal{M}_{\varphi,B}$ associated to a essentially nondecreasing function
$\varphi$ and to a submultiplicative Young function $B$.