  We first give the local well-posedness of strong solutions to the Cauchy
problem of the 3D two-fluid MHD equations, then study the blow-up criterion of
the strong solutions. By means of the Fourier frequency localization and Bony's
paraproduct decomposition, it is proved that strong solution $(u,b)$ can be
extended after $t=T$ if either $u\in L^q_T(\dot B^{0}_{p,\infty})$ with
$\frac{2}{q}+\frac{3}{p}\le 1$ and $b\in L^1_T(\dot B^{0}_{\infty,\infty})$, or
$(\omega, J)\in L^q_T(\dot B^{0}_{p,\infty})$ with $\frac{2}{q}+\frac{3}{p}\le
2$, where $\omega(t)=\na\times u $ denotes the vorticity of the velocity and
$J=\na\times b$ the current density.
