Quine (1975) observed that theories that are intuitively classified as mere notational variants of each other (e.g. by permutation of their theoretical vocabulary) may be jointly inconsistent in the technical sense without being incompatible in any substantial sense. More generally, he suggested that theories that can (in a certain sense) be translated into each other are not incompatible, but only different formulations of one and the same theory. They are, as we would say today, theoretically equivalent. The underdetermination thesis Quine (1975) came to consider was that, for any theory, there are two theories empirically equivalent to the former that are jointly inconsistent but not theoretically equivalent. For him, the truth of this thesis was an open question. As far as I know, it still is on his notion of theoretical equivalence. Another notion of theoretical equivalence was proposed by Glymour (1970). In recent years, these and other notions have been suggested and studied by Barrett and Halvorson (2016) and Lefever and Székely (2019). In my talk, I will investigate various notions of theoretical equivalence in relation to Quine's underdetermination thesis.