The steady motion of a Janus drop under a uniform external flow is considered. First, we analyze the equilibrium shape of a Janus-like drop in a motionless ambient fluid, i.e., the special case of a nearly spherical compound drop with a nearly flat internal interface. This configuration is realizable when the liquids comprising the drop have close interfacial tensions with the ambient fluid, but a small interfacial tension between each other. Then, we consider the flow past a perfect Janus drop composed of two hemispherical domains each occupied by a different fluid. For the sake of simplicity, all the interfaces are assumed nondeformable. The problem is solved both analytically, by means of the Lamb expansion, and numerically. The relation between the flow velocity and the force imposed on the drop, which is a generalization of the classical Hadamard–Rybczynski formula, is found. A torque is also imposed on the drop in the general case. The stable regime of motion of a torque-free drop is found to be axisymmetric, with the less viscous fluid at the upstream face. For this particular configuration, the deformation of the internal interface is also found employing a perturbation technique, whereas the distortion of the drop surface can be safely neglected.