Two incremental approaches are available in the literature to identify the kinetics of either homogeneous or fluid-fluid reaction systems from transient concentration measurements. The first approach decomposes the identification task into a sequence of subtasks to identify sequentially the reaction and mass-transfer flows, the reaction and mass-transfer rates, and the rate parameters. The approach is of the "differential" type, because the reaction and mass-transfer rates are estimated through numerical differentiation of concentration measurements. The second approach, which is of the "integral" type, is based on the concept of extents. The present paper compares the well-known simultaneous approach and these two incremental approaches with respect to (i) the minimum number of species for which concentration measurements must be available, (ii) their ability to discriminate among competing rate laws, (iii) the accuracy of the estimated rate parameters, and (iv) the associated computational effort. The last three issues are investigated in a numerical study via the simulated start-up of a homogeneous continuous stirred-tank reactor. (C) 2012 Elsevier Ltd. All rights reserved.