In this paper, we present a numerical investigation of various types of drops detaching from an axisymmetric, laminar compound jet of immiscible fluids. The compound jet flows in a co-flowing 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 and Newtonian fluids. Numerical results show that depending on flow parameters, the compound jet can break up into different types of drops: simple drops, single-core compound drops and multi-core compound drops.