The paper is concerned with identification of the key mechanisms controlling deflagration-to-detonation transition in unconfined gaseous systems. The issue of thermal runaway triggered by positive feedback between the advancing flame and the flame-driven precompression wave is discussed in the context of expanding spherical flames. Depending on parameters of the system the transition may occur either within a subsonic or supersonic range of flame propagation. The paper is an extension of the previous study concerned with planar flames. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.