  Among all classes of pseudo-differential operators only the Weyl operators
enjoy the property of symplectic covariance with respect to conjugation by
elements of the metaplectic group. In this paper we show that there is,
however, a weaker form of symplectic covariance for Shubin's {\tau}-dependent
operators, in which the intertwiners no longer are metaplectic, but still are
invertible non-unitary operators. We also study the case of Born--Jordan
operators, which are obtained by averaging the {\tau}-operators over the
interval [0,1] (such operators have recently been studied by Boggiatto and his
collaborators). We show that metaplectic covariance still hold for these
operators, with respect top a subgroup of the metaplectic group.
