A group of Muslims in northern Texas has created what may be the first official Shariah law system in the United States.

The new Shariah tribunal in Irving, Texas, is trying to assure Americans they're not planning to follow the type of Shariah law practiced in Muslim countries. But critics aren't convinced.

Dr. Frank Gaffney, who leads the Center for Security Policy in Washington, D.C., has studied what happens when Shariah law enters into state court decisions.

"I think what we will see is a coercion of Muslims to participate in this program," he said.

If Shariah law continues to encroach into our legal system, how might if affect the constitutional rights of Americans, particularly women? Dr. Gaffney explains more.

Gaffney said he thinks that some in the Muslim community think they're following Shariah law to some extent, but they're not following the authoritative version of it.

"Which is a brutally repressive - very hostile to women, hostile to homosexuals, hostile to Jews, hostile to Christians - kind of totalitarian system," he said.

CSP has found that at least 146 cases have been identified where the U.S. court system has allowed a Shariah court to adjudicate.

"In about 20 percent of those cases the court agreed to use Shariah instead of American laws with our constitutional gaurantees respected," Gaffney said.

In some Muslim countries, severe punishments are common, women have very few rights, and blasphemy against Mohammed can result in a death sentence.

But Tribunal Judge Imam Moujahed Bakhach is denying that will happen in America.

"The misconception about what they see through the media is that Shariah means cut the head, chop the heads, cut the hands and we are not in that," he said. "We are not here to invade the White House or invade Austin."

But Robert Spencer of JihadWatch writes: "There is no school of Islamic jurisprudence among either Sunnis or Shites that does not mandate stoning for adultery, amputation of the hand for theft, and the subjugation of women."

Imam Bakhach and three other Muslim judges are planning to bypass the traditional legal system of Texas to handle civil cases on their own.

They plan to start by administering their own rulings for cases like divorce and business disputes.

But critics caution that allowing Shariah tribunals to operate in the U.S. essentially allows Islamic law to replace U.S. law, and will undermine the established U.S. rights of some of the victims.

The Center for Security Policy issued a report in 2011, documenting how Shariah law is already being applied in official state courts across America.

"The facts are the facts: some judges are making decisions deferring to Shariah law even when those decisions conflict with constitutional protections," the group states.

The report discovered 50 such cases involving "Muslim American families, mostly Muslim women and children, who were asking American courts to preserve their rights to equal protection and due process."

"These families came to America for freedom from the discriminatory and cruel laws of Shariah. When our courts then apply Shariah law in the lives of these families, and deny them equal protection, they are betraying the principles on which America was founded," the Center for Security Policy states.

Spencer agrees, pointing out that is the track record of Shariah around the world.

"Sharia polities throughout history and today have denied the freedom of speech and the freedom of conscience, and they have mandated discrimination against women and non-Muslims," Spencer says.