We investigate the possibility of forming deeply bound ultracold RbCs molecules by a two-color photoassociation experiment. We compare the results with those for Rb₂ in order to understand the characteristic differences between heteronuclear and homonuclear molecules. The major differences arise from the different long-range potential for excited states. Ultracold ⁸⁵Rb and ¹³³Cs atoms colliding on the X ¹Σ⁺ potential curve are initially photoassociated to form excited RbCs molecules in the region below the Rb(5S)+Cs(6P_1/2) asymptote. We explore the nature of the Ω=0⁺ levels in this region, which have mixed A ¹Σ⁺ and b ³Π character. We then study the quantum dynamics of RbCs by a time-dependent wavepacket (TDWP) approach. A wavepacket is formed by exciting a few vibronic levels and is allowed to propagate on the coupled electronic potential energy curves. We calculate the time dependence of the overlap between the wavepacket and ground-state vibrational levels. For a detuning of 7.5 cm⁻¹ from the atomic line, the wavepacket for RbCs reaches the short-range region in about 13 ps, which is significantly faster than for the homonuclear Rb₂ system; this is mostly because of the absence of an R⁻³ long-range tail in the excited-state potential curves for heteronuclear systems. We give a simple semiclassical formula that relates the time taken to the long-range potential parameters. For RbCs, in contrast to Rb₂, the excited-state wavepacket shows a substantial peak in singlet density near the inner turning point, and this produces a significant probability of de-excitation to form ground-state molecules bound by up to 1500 cm⁻¹. The short-range peak depends strongly on non-adiabatic coupling and is reduced if the strength of the spin–orbit coupling is increased. Our analysis of the role of spin–orbit coupling concerns the character of the mixed states in general and is important for both photoassociation and stimulated Raman de-excitation.