During composting of livestock manure, transformations of organic matter result in gaseous emissions, which can harm the environment. Two experiments were done in enclosures to measure the fluxes of NH3, N2O, CO2, CH4 and H2O emitted by 8 heaps of compost representing the range of biodegradability of nitrogen and carbon in the livestock manure. The heaps were monitored for the first 2 months, corresponding to the thermophilic phase during which nearly all-mass losses occur. Four parameters describe the NH3 emission kinetics and the main influential factors were noted: (1) the response time to reach maximum intensity is affected mainly by the initial micro-flora; (2) the amplitude depends mainly on C biodegradability and also on micro-flora; (3) the emission duration depends mainly on N biodegradability; and (4) the cumulative emission, which varied from 16.5 to 48.9% of the nitrogen initially present in the heap, depends both on C and N biodegradability. A predictive model for NH3 and CO2 emissions for the thermophilic phase of the composting of livestock manure is proposed. The variability in cumulative emissions of CO2 and of NH3 is well explained by the contents of soluble elements and hemicellulose in the dry matter (Van Soest fractioning), and soluble nitrogen (12 h extraction at 4°C in water). In our conditions of favourable aeration and humidity, N2O and CH4 emissions were low. The role of the biodegradable carbon in reducing NH3 emission is highlighted.