Context. The microquasar GX 339−4 experienced a new outburst in 2010: it was observed simultaneously at various wavelengths from radio up to soft γ-rays. We focus on observations that are quasi-simultaneous with those made with the INTEGRAL and RXTE satellites: these were collected in 2010 March–April during our INTEGRAL target of opportunity programme, and during some of the other INTEGRAL observing programmes with GX 339−4 in the field-of-view. Aims. X-ray transients are extreme systems that often harbour a black hole, and are known to emit throughout the whole electromagnetic spectrum when in outburst. The goals of our programme are to understand the evolution of the physical processes close to the black hole and to study the con...