Although the law relating to anti-suit injunctions (and by extension anti-anti-suit injunctions) is mostly settled since the decision of the High Court in CSR Ltd v Cigna Insurance Australia Ltd (1997) 189 CLR 345, uncertainty still remains as to the effect of a claim under the TPA on whether a court issues an anti-suit injunction or stays its proceedings.
Applying CSR v Cigna Insurance, the fact that a TPA claim may be heard in an Australian court but not in a foreign court may be a factor weighing against awarding a stay and weighing in favour of issuing an anti-suit or anti-anti-suit injunction. So much was recognised in Pan Australian Shipping Pty Ltd v The Ship “Comandate”  FCA 881, where Rares J concluded that a TPA claim was an important consideration when a court was considering jurisdictional issues.
More recently, Australian courts have stayed proceedings and refused to award anti-suit or anti-anti-suit injunctions even though a TPA claim has been raised (see Armacel Pty Ltd v Smurfit Stone Container Corporation  FCA 592, Bella Products Pty Ltd v Creative Designs International Ltd  FCA 868 and Nicola v Ideal Image Development Corporation Inc (2009) 261 ALR 1). However, in all these cases the courts emphasised that the TPA claims were going to be pursued in the foreign proceedings and the parties agreed to do so. In Armacel, for example, Jacobson J stressed that the essential question in deciding whether to award a stay was whether Armacel was able to obtain relief under the TPA in the United States proceedings; if not, a stay may not have been granted.