Dynamic behavior and 3D spatial structure of low-Lewis-number counterflow premixed flames are numerically studied in the frame of thermo-diffusive model with one-step chemical reaction. The diverse combustion regimes are described and regions of existence of these regimes in equivalence ratio/stretch rate plane are identified. Qualitative comparison between numerical results and results of microgravity experiments are discussed. Experiments and numerical simulations demonstrate that at small stretch rate conditions lean low-Lewis-number counterflow flames can appear as a set of separate ball-like flames in a state of chaotic motion. The extension of extinction limits associated with existence of sporadic combustion regimes is observed. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.