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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 metricwith 3 arbitrary parameters we find a rotating metric $g_{\mu\nu}$ with 4 suchparameters $(M, a, Q_E, Q_M)$, and then a solution with this $g_{\mu\nu}$ asmetric. 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 solutionwe have found the $S-$duality transformation we get a new solution, whoseaxion, dilaton and vector fields have one more parameter. The metric, eachvector field and the $\lambda=\xi+ie^{-2\phi}$ of our solutions and thesolution 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 thesame 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 fromour solutions a number of known solutions can be obtained, which together withour solutions are listed in an Appendix. Also it is shown that all solutionswhich are mentioned in the paper satisfy all energy conditions, and massformulae are obtained for them.

Rotating Black Hole Solutions with Axion Dilaton and Two Vector Fields and Solutions with Metric and Fields of the Same Form