We investigate the asymptotic behavior for type II Hermite–Padé approximation to two functions, where each function has two branch points and the pairs of branch points are separated. We give a classification of the cases such that the limiting counting measures for the poles of the Hermite–Padé approximants are described by an algebraic function h of order and genus 0. This situation gives rise to a vector-potential equilibrium problem for measures λ, μ₁, and μ₂, and the poles of the common denominator are asymptotically distributed like λ/2. We also work out the strong asymptotics for the corresponding Hermite–Padé approximants by using a 3 × 3 Riemann–Hilbert problem that characterizes this Hermite–Padé approximation problem.