Four members of the Zapon family — a husband and wife and their two elder children (collectively “Zapons”) appeal the denial of them application for an award of attorney’s fees against the United States under the Equal Access to Justice Act (“EAJA,” 28 U.S.C. § 2412 (d)(1)(A)). EAJA is not an automatic fee-shifting statute in favor of litigants who prevail against the government. Instead Section 2412(d)(1)(A) says that such a prevailing party is not entitled to an award if “the court finds that the position of the United States was substantially justified or that special circumstances make an award unjust.” That “substantially justified” concept has been fleshed out in Pierce v. Underwood, 487 U.S. 552, 565 , 108 S.Ct. 2541, 2550 , 101 L.Ed.2d 490 (1988), followed in Commissioner v. Jean, 496 U.S. 154 , 158 n. 6, 110 S.Ct. 2316 , 2319 n. 6, 110 L.Ed.2d 134 (1990).

In terms of the underlying substantive merits, both the magistrate judge and the district court were correct in concluding that the Board of Immigration Appeals abused its discretion in refusing to grant Zapons a stay of deportation: Under a then-recently-enacted amendment to the Immigration and Nationality Act (8 U.S.C. § 1252b(c)(3)(B)), the filing of a motion to reopen deportation proceedings where the alien had not been given notice of such proceedings automatically stays deportation. In this instance the Immigration Judge had conducted a deportation hearing in absentia without realizing that Zapons had not received notice of that hearing (something that obviously explained their failure to appear). Then, despite the pendency of a motion to reopen, the immigration authorities actively pursued Zapons with a view toward deporting them.

But Zapons’ difficulty in recovering under EAJA stems from their having gone fugitive in the face of a still-outstanding (though wrongfully issued) deportation order. They complain that the deportation order created a Catch-22 dilemma because surrendering would have triggered their immediate deportation, mooting their meritorious attack on the order’s validity. But federal courts regularly grant emergency relief against arbitrary rulings in immigration procedures (which, judging by the reported eases and by judicial experience, do seem to produce far more than their share of arbitrariness), and Zapons did not immediately attempt to avail themselves of that opportunity rather than going fugitive.

Only in the rarest of situations do federal courts countenance a party’s disregard of an existing court order because it was mistakenly issued — a clearly invalid pri- or restraint in the First Amendment context, “where the injunction was transparently invalid or had only a frivolous pretense to validity,” is the only example that comes to mind. Walker v. City of Birmingham, 388 U.S. 307, 315 , 87 S.Ct. 1824, 1829 , 18 L.Ed.2d 1210 (1967). In all other situations obedience to even an assertedly void (not merely voidable) order is required unless and until it has been vacated or reversed. Walker, id. at 320-21, 87 S.Ct. at 1832 ; United States v. United Mine Workers, 330 U.S. 258, 290-94 , 67 S.Ct. 677, 694-96 , 91 L.Ed. 884 (1947); Hugh Cox, The Void Order and the Duty To Obey, 16 U.Chi.L.Rev. 86 (1948).

Here Zapons engaged in self-help rather than complying with an outstanding order to surrender for deportation, and the immigration authorities responded by denying a stay of deportation. As Bar-Levy v. United States Dep’t of Justice, 990 F.2d 33, 35 (2d Cir.1993) (citations omitted) has put it:

In light of that prestigious court’s pronouncement and the similar circumstances of this case, it can scarcely be said that the United States was not “substantially justified” in opposing Zapons’ efforts to obtain a stay of deportation.

We therefore AFFIRM.

. Zapons urge that only two of the four family members were literally fugitives as a matter of law, because only they had been the subject of the final deportation order. But the situation was more complex than that: All four Zapons had been noticed to report initially, then all four filed motions to reopen that triggered the automatic statutory stay (also filing applications for a stay at the same time). Whether because only the two daughters had paid the necessary fee or otherwise, the ensuing notice to report for deportation was directed only to two of the four family members. All four then sought habeas corpus, were then notified to report for deportation and then succeeded in obtaining a stay from the Magistrate Judge. In that convoluted state of affairs, it was reasonable for the courts below to apply the "substantial justification” and "special circumstances” criteria across the board. . Indeed, it was their later-filed habeas petition that spared Zapons from deportation.