It is normally accepted among nations that “territorial jurisdiction” is based on a crimes committed within the territory of a sovereign state. However, sometimes states also exercise jurisdiction based on a crimes that was committed abroad by one of their nationals or because the crime was a national of the state. For instance, in the federal court case United States v. Fawaz Yunis, in which five men hijacked a Jordanian airliner, the U.S. took jurisdiction based in nationality of the victim. Yunis was charged with violations of U.S. statutes, 18 U.S.C 1203 Hostage Taking, and U.S.C. jurisdiction 32(a) jurisdiction over aircraft in overseas of foreign air commerce” and 32 (b) jurisdiction over offenders later “found” in the U.S.

On appeal, Yunis, a Lebanese resident and citizen, argued that the federal law provided no independent basis for jurisdiction, and with regards to the general principles of international law; the court also lacked subject matter and personal jurisdiction over a crime committed by a nonresident alien on foreign soil. However, the court sustained that in article 1 section 18, clause 10 of the Constitution, which gives congressional power to enact legislation on extraterritorial jurisdiction, the power to “define and punish piracies and felonies committed on the high seas and offenses against the law of nations”.
Moreover, the Yunis case basis for jurisdictional demonstrates the lack both an international basis as well as domestic link for jurisdiction. Thus, under subsection (b), of the Hostage Taking statute which applies to acts of violence against any individual on board “any civil aircraft registered in a country other that the Unites States … if the offender is found in the United States”, contradicts the Yunis situation. Indeed, Yunis was not “found” in the United States within the meaning of the statute in that the cunning manner in which the federal agents used to obtain his arrest, and forcibly transport him to the U.S., eliminates any jurisdiction under the statute. In fact, the statute neither stops nor approves any extension of jurisdiction over offenders who were brought into the country by force. Also, in acknowledging the circumstances, this action is in contradictory to that of the United States constitution 5th and 14th amendment of the Due Process clause. With regards to the international law this action is also contrary to the norms of international law to bring someone to the United States by “force” to be charged with and offense over which the U.S. had jurisdiction only when he was found inside U.S. territory.
The concept of apprehending terrorists and bringing them to justice has been developed as major standard of U.S. counterterrorism strategy, therefore, granting permission to exercise extra territorial jurisdiction. Although previous cases such as United States v. Bowman have set the phase for such jurisdiction, in which the court projected that there was no constitutional bar to the extraterritorial application of penal laws, has, however, raise the concern concerning respect for sovereignty. This involves the act of capturing and returning to the U.S. as suspected terrorists, even it the suspect is in another country and the host country does not grant permission for such activity. Reliance on U.S. law and international legal principles makes it a model for future prosecution of terrorists in the United States. This case brings our attention to the U.S. application of domestic law, in which such application to aliens, as well as finding a resolution on constitutional claims during trial is sovereign.
In conclusion, this case demonstrates the deviation of customary law, in which a state relies on its own law and legislature in attempt to coffer jurisdiction which the state does not in fact posses. In this case, the U.S. has accepted the passive personality principle as sufficient bases under international law for it to assert jurisdiction over extraterritorial crime, represents the evolving strategy for dealing with the apprehension and prosecution of terrorists as criminals.

The first couple of problems are matters of number agreement. eg. a is singular therefore the noun crime must also be singular.

is based on a crime

However, sometimes use "nations" here also exercise jurisdiction based on a crime that was committed abroad by one of their citizens or ( - this phrase is not clear- because the crime was national of the state. )

jurisdiction based on the nationality of the victim

The rest of the paragraphs look pretty good!