  In a recent paper (1994 {\sl J.\ Phys.\ A: Math.\ Gen.\ }{\bf 27} 5907), Oh
and Singh determined a Hopf structure for a generalized $q$-oscillator algebra.
We prove that under some general assumptions, the latter is, apart from some
algebras isomorphic to su$_q$(2), su$_q$(1,1), or their undeformed
counterparts, the only generalized deformed oscillator algebra that supports a
Hopf structure. We show in addition that the latter can be equipped with a
universal $\cR$-matrix, thereby making it into a quasitriangular Hopf algebra.
