  A supersymmetric extension of the two-phase fluid flow system is formulated.
A superalgebra of Lie symmetries of the supersymmetric extension of this system
is computed. The classification of the one-dimensional subalgebras of this
superalgebra into 63 equivalence conjugation classes is performed. For some of
the subalgebras, it is found that the invariants have a non-standard structure.
For six selected subalgebras, the symmetry reduction method is used to find
invariants, orbits of the subgroups and reduced systems. Through the solutions
of the reduced systems, the most general solutions are expressed in terms of
arbitrary functions of one or two fermionic and one bosonic variables.
