  We present two rotating black hole solutions with axion $\xi$, dilaton $\phi$
and two U(1) vector fields. By applying the "Newman-Janis trick" to a metric
with 3 arbitrary parameters we find a rotating metric $g_{\mu\nu}$ with 4 such
parameters $(M, a, Q_E, Q_M)$, and then a solution with this $g_{\mu\nu}$ as
metric. Our solution is asymptotically flat and has angular momentum $J=M a$,
gyromagnetic ratio $g=2$, two horizons, the singularities of Kerr's solution,
axion and dilaton singular only for $r=a\cos\theta=0$. Applying to the solution
we have found the $S-$duality transformation we get a new solution, whose
axion, dilaton and vector fields have one more parameter. The metric, each
vector field and the $\lambda=\xi+ie^{-2\phi}$ of our solutions and the
solution of : Sen for $Q_E$, Sen for $Q_E$ and $Q_M$, Kerr-Newman for $Q_E$ and
$Q_M$, Kerr, Ref. 9, STW, GM-GHS, Reissner-Nordstr\"{o}m,Schwarzschild are the
same function of $a$, and two functions $\rho^2=r(r+b)+a^2\cos^2\theta$ and
$\Delta=\rho^2-2Mr+c$, of $a$, $b$ and two functions, and of $a$, $b$ and $d$
respectively, where $a$, $b$, $c$ and $d$ are constants. It is shown that from
our solutions a number of known solutions can be obtained, which together with
our solutions are listed in an Appendix. Also it is shown that all solutions
which are mentioned in the paper satisfy all energy conditions, and mass
formulae are obtained for them.
