There have been concerns about whether the US has jurisdiction over the private contractors which allegedly took place in the torture of Iraqui prisoners of war.
The following are some of the relevant sections from the US Code that would apply to those contractors (as well as to members of the military). As you can see, US courts have jurisdiction over private contractors who are American citizens by virtue of (at least) 18 USC Sec. 2340A and Sec. 2441. They may also have jurisdiction under 18 USC Sec. 3261 - if so, this would cover both American and non-American contractors.
18 USC Sec. 2340A
(a) Offense. - Whoever outside the United States commits or
attempts to commit torture shall be fined under this title or
imprisoned not more than 20 years, or both, and if death results to
any person from conduct prohibited by this subsection, shall be
punished by death or imprisoned for any term of years or for life.
(b) Jurisdiction. - There is jurisdiction over the activity
prohibited in subsection (a) if -
(1) the alleged offender is a national of the United States; or
(2) the alleged offender is present in the United States,
irrespective of the nationality of the victim or alleged
offender.
(c) Conspiracy. - A person who conspires to commit an offense
under this section shall be subject to the same penalties (other
than the penalty of death) as the penalties prescribed for the
offense, the commission of which was the object of the conspiracy.
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18 USC Sec. 2441
(a) Offense. - Whoever, whether inside or outside the United
States, commits a war crime, in any of the circumstances described
in subsection (b), shall be fined under this title or imprisoned
for life or any term of years, or both, and if death results to the
victim, shall also be subject to the penalty of death.
(b) Circumstances. - The circumstances referred to in subsection
(a) are that the person committing such war crime or the victim of
such war crime is a member of the Armed Forces of the United States
or a national of the United States (as defined in section 101 of
the Immigration and Nationality Act).
(c) Definition. - As used in this section the term ''war crime''
means any conduct -
(1) defined as a grave breach in any of the international
conventions signed at Geneva 12 August 1949, or any protocol to
such convention to which the United States is a party;
(2) prohibited by Article 23, 25, 27, or 28 of the Annex to the
Hague Convention IV, Respecting the Laws and Customs of War on
Land, signed 18 October 1907;
(3) which constitutes a violation of common Article 3 of the
international conventions signed at Geneva, 12 August 1949, or
any protocol to such convention to which the United States is a
party and which deals with non-international armed conflict; or
(4) of a person who, in relation to an armed conflict and
contrary to the provisions of the Protocol on Prohibitions or
Restrictions on the Use of Mines, Booby-Traps and Other Devices
as amended at Geneva on 3 May 1996 (Protocol II as amended on 3
May 1996), when the United States is a party to such Protocol,
willfully kills or causes serious injury to civilians.
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18 USC Sec. 3261
(a) Whoever engages in conduct outside the United States that
would constitute an offense punishable by imprisonment for more
than 1 year if the conduct had been engaged in within the special
maritime and territorial jurisdiction of the United States -
(1) while employed by or accompanying the Armed Forces outside
the United States; or
(2) while a member of the Armed Forces subject to chapter 47 of
title 10 (the Uniform Code of Military Justice),
shall be punished as provided for that offense.