The majority of intracellular signalling cascades in higher eukaryotes are initiated by GPCRs (G-protein-coupled receptors). Hundreds of GPCRs signal through a handful of trimeric G-proteins, raising the issue of signal specificity. In the present paper, we illustrate a simple kinetic model of G-protein signalling. This model shows that stable production of significant amounts of free Galpha(GTP) (GTP-bound Galpha subunit) and betagamma is only one of multiple modes of behaviour of the G-protein system upon activation. Other modes, previously uncharacterized, are sustained production of betagamma without significant levels of Galpha(GTP) and transient production of Galpha(GTP) with sustained betagamma. The system can flip between different modes upon changes in conditions. This model demonstrates further that the negative feedback of receptor uncoupling or internalization, when combined with a positive feedback within the G-protein cycle, under a broad range of conditions results not in termination of the response but in relaxed oscillations in GPCR signalling. This variety of G-protein responses may serve to encode signal specificity in GPCR signal transduction.