  We study the quadratic integral points-that is, (S-)integral points defined
over any extension of degree two of the base field-on a curve defined in P_3 by
a system of two Pell equations. Such points belong to three families explicitly
described, or belong to a finite set whose cardinality may be explicitly
bounded in terms of the base field, the equations defining the curve and the
set S. We exploit the peculiar geometry of the curve to adapt the proof of a
theorem of Vojta, which in this case does not apply.
