Experimental and numerical study of the detonation has been conducted in heterogeneous reactive twophase media made of liquid isooctane sprays dispersed in gaseous oxidizing atmospheres. Influence of the oxidizer composition on conditions of detonation formation and propagation regimes, with particular attention on the existence of the so-called cellular structure, has been studied. Experiments have been performed under standard initial conditions of temperature and pressure (293 K, 1 bar) in a 4-m long vertical, square cross-section (53 x 53 mm(2)) detonation tube. The mean isooctane droplet size was of about 30 pm. When oxidizing mixture was made of air (O-2 + beta N-2 with beta = 3.76), three detonation regimes have been observed with increasing equivalence ratio: a spinning regime, a marginal one with half a cell structure, and a normal multi-headed detonation regime. At smaller dilution ratio (beta = 2 and 1), only the multi-headed detonation regime was observed, with smaller cell size. When nitrogen is replaced by argon as inert diluent, the detonation structure is multi-headed; the cellular structure is more regular and the cell size is smaller than with nitrogen. Numerical simulations have been performed with the EFAE code, with taking in consideration the chemical composition of the oxidizing phase and the effects of the two-phase mixture richness. Results of 2D and 3D numerical simulations, as a function of the equivalence ratio and the dilution, display propagation regimes and detonation cell sizes in reasonable agreement with the experimental results. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.