Laser-induced fluorescence spectra of the 3(0)3 K-0(1) and 3(0)4 K-0(1) vibronic bands of the A 1A(u) <-- X 1SIGMA(g)+ transition in acetylene have been recorded with a resolution of 18 MHz. Each rotational transition consists of a group of lines due to coupling of the electronically excited singlet state with isoenergetic triplet states. Using the standard deconvolution procedure the singlet-triplet coupling elements and the density of coupled triplet states are derived for rotational levels up to J=4 in both bands. From the density of coupled triplet states it is concluded that the A 1A(u) state is perturbed by the T1 B-3(2) state. Magnetic field measurements have shown that the predissociation of acetylene in the 4nu3' vibrational level of the A state is caused by a coupling via the T1 B-3(2) state with predissociating vibrational levels of the electronic ground state.