Several researchers have reported that under certain conditions, forest fires with normal behavior suddenly start to propagate at unusual and very high rate of spread. Over the last decades, these accelerating forest fires were responsible for many fatalities in Europe. A thermochemical approach, based on the ignition of a volatile organic compounds (VOCs) cloud, has been proposed previously to explain this phenomenon. Indeed, some vegetal species emit volatile substances when they are heated. A typical Mediterranean plant, Rosmarinus officinalis, emits 14 components, mainly alpha-pinene and limonene. The acceleration of the rate of spread can be the consequence of the ignition of these emitted gases. The determination of alpha-pinene/air and limonene/air premixed flame speeds is essential to take into account this approach in forest fire modeling. It is the main purpose of this article. The spherical expanding flames methodology coupled with a nonlinear model was used to determine the unstretched premixed flame speeds of the two major compounds involved in accelerating forest fires. Experiments were performed in a spherical vessel at atmospheric pressure. The results for different equivalence ratios and unburned gas temperatures are given for the first time. The unstretched premixed flame speeds are discussed relatively to rates of spread of three real accidents.