  The properties of the Pastro polynomials on the real line are studied with
the help of a triplet of $q$-difference operators. The $q$-difference equation
and recurrence relation these polynomials obey are shown to arise as
generalized eigenvalue problems involving the triplet of operators, with the
Pastro polynomials as solutions. Moreover, a discrete biorthogonality relation
on the real line for the Pastro polynomials is obtained and is then understood
using adjoint operators. The algebra realized by the triplet of $q$-difference
operators is investigated.
