We present a numerical investigation of breakup modes of an axisymmetric, laminar compound jet of immiscible fluids, which flows in a coflowing immiscible outer fluid. We use a front-tracking/finite difference method to track the unsteady evolution and breakup of the compound jet, which is governed by the Navier-Stokes equations for incompressible Newtonian fluids. Numerical results show that depending on parameters such as the Reynolds number Re (in the range of 5-30) and Weber Number We (in the range of 0.1-0.7), based on the inner jet radius and inner fluid properties, the compound jet can break up into drops in various modes: inner dripping-outer dripping (dripping), inner jetting-outer jetting (jetting), and mixed dripping-jetting. Decreasing Re or increasing We promotes the jetting mode. The transition from dripping to jetting is also strongly affected by the velocity ratios, U-21 (intermediate to inner velocities) and U-31 (outer to inner velocities). Increasing U-21 makes the inner jet thinner and stretches the outer jet and thus promotes jetting. In contrast, increasing U-31 thins the outer jet, and thus, when the inner jet is dripping, the outer jet can break up into drops in the mixed dripping-jetting mode. Continuously increasing U-31 results in thinning both inner and outer jets and thus produces small drops in the jetting mode. In addition, starting from dripping, a decrease in the interfacial tension ratio of the outer to inner interfaces results in the mixed dripping-jetting and jetting modes. These modes produce various types of drops: simple drops, and compound drops with a single inner drop (single-core compound drops) or a few inner drops (multi-core compound drops). (C) 2012 Elsevier Ltd. All rights reserved.