  In this work we study various aspects of supersymmetric three-dimensional
higher-derivative field theories. We classify all possible models without
derivative terms in the auxiliary field of the fermionic sector and find that
scalar field theories of the form $P(X,\phi)$, where $X=-(\partial\phi)^2/2$,
belong to this kind of models. A ghost-free supersymmetric extension of
Galileon models is found in three spacetime dimensions. Finally, the auxiliary
field problem is discussed.
