The 4503 rovibronic term values belonging to the mutually perturbed A 1 Σ + u and b 3 Πu states of Cs2 were extracted from laser induced fluorescence (LIF) A ∼ b → X 1 Σ + g Fourier transform spectra with the 0.01 cm −1 uncertainty. The experimental term values of the A 1 Σ + u ∼ b 3 Πu complex covering the rotational levels J ∈ [4, 395] in the excitation energy range [9655, 13630] cm −1 were involved into coupled-channel (CC) deperturbation analysis. The deperturbation model takes explicitly into account spin-orbit coupling of the A 1 Σ + u (A0 + u ) and b 3 Π + 0u (b0 + u ) states as well as spin-rotational interaction between the Ω = 0, 1 and 2 components of the b 3 Π + Ωu state. The ab initio relativistic calculations on the low-lying electronic states of Cs2 were accomplished in the framework of Fock space relativistic coupled cluster (FSRCC) approach to provide the interatomic potentials of the interacting A0 + u and b0 + u states as well as the relevant A ∼ b spin-orbit coupling function. To validate the present CC deperturbation analysis solely obtained by energy-based data, the A ∼ b → X(v ′′ X ) LIF intensity distributions were measured and compared with their theoretical counterparts obtained by means of the non-adiabatic vibrational wave functions of the A ∼ b complex and the FSRCC A ∼ b → X transition dipole moments calculated by the finite-field method.