We review the construction of supersymmetric extension of the n-particle Euler-Calogero-Moser model within the Hamiltonian approach [1]. The main feature of the proposed supersymmetrization method is that it is automatically adapted for a model with an arbitrary even number of supersymmetries. It is shown that the number of fermions that must be used in this construction is 1/2N n(n+1). We demonstrate that the resulting supersymmetric system is dynamically invariant with respect to the superconformal group and give the explicit realization of its generators in terms of the conserved currents. For the simplest case of the supersymmetric n-particle Euler-Calogero-Moser model we provide its description in superspace by using the corresponding constrained superfields. © 2019 Published under licence by IOP Publishing Ltd.