  The family of Tremblay-Turbiner-Winternitz Hamiltonians $H_k$ on a plane,
corresponding to any positive real value of $k$, is shown to admit a ${\cal N}
= 2$ supersymmetric extension of the same kind as that introduced by Freedman
and Mende for the Calogero problem and based on an ${\rm osp}(2/2, \R) \sim
{\rm su}(1,1/1)$ superalgebra. The irreducible representations of the latter
are characterized by the quantum number specifying the eigenvalues of the first
integral of motion $X_k$ of $H_k$. Bases for them are explicitly constructed.
The ground state of each supersymmetrized Hamiltonian is shown to belong to an
atypical lowest-weight state irreducible representation.
