Starting from the Hamiltonian formulation of N = 2 supersymmetric Calogero models associated with the classical An, Bn, Cn and Dn series and their hyperbolic/trigonometric cousins, we provide their superspace description. The key ingredients include n bosonic and 2n(n−1) fermionic N = 2 superfields, the latter being subject to a nonlinear chirality constraint. This constraint has a universal form valid for all Calogero models. With its help we find more general supercharges (and a superspace Lagrangian), which provide the N = 2 supersymmetrization for bosonic potentials with arbitrary repulsive two-body interactions.