RAYMONDVILLE, Texas -- Two illegal immigrants from Mexico who were charged with first-degree murder in the shooting death of an off-duty U.S. Border Patrol agent in front of his family in Texas have been arrested and deported numerous times, police sources told FoxNews.com.

One suspect has been arrested no fewer than four times for entering the U.S. illegally, according to federal court records. The other has been deported twice after entering the U.S. illegally, sources said.

Gustavo Tijerina, 30, and Ismael Hernandez, 40, were arraigned Tuesday afternoon inside the Willacy County jail library. They were ordered held without bail after being charged with capital murder of a peace officer, attempted murder, and a variety of lesser charges.

The pair, who have been living in Texas illegally, confessed after being interviewed multiple times Monday to killing Border Patrol agent Javier Vega Jr. in front of his wife and two kids and his parents Sunday night while they were fishing in Santa Monica, Sheriff Larry Spence told FoxNews.com. The National Border Patrol Council, the union that represented Vega, has set up a memorial fund on behalf of his widow and three young children.

They finally confessed to the robbery and indicated they knew they had killed someone, but did not know it was an off-duty Border Patrol agent, Spence said in an interview in his office Tuesday morning.

"They do now," he said.

When asked how the suspects reacted when they learned the victim was a Border Patrol agent, Spence said, "shock and concern."

The sheriff said the two suspects were likely connected to cartels or other criminal gangs.

"They claim to have been involved in other incidents, this means you've got stolen vehicles going into Mexico," he said.

"Everything is going to be cartel-related, there's a connection somehow.

"This is not the first episode of border violence in Willacy County but it's the first time someone's been killed," he said.

Tijerina, who according to records was arrested at least four times between 2007 and 2010 for entering the U.S. illegally, and Hernandez allegedly approached Vega and his family and tried to rob them on Sunday night. When Vega pulled out his weapon, the suspects allegedly shot him in the chest, killing him.Vega's father was shot in the hip and is recovering at a nearby hospital.

Both Tijerina and Hernandez were arraigned on seven charges: capital murder of a peace officer, attempted murder, four counts each of aggravated robbery and one count of tampering with evidence. When asked by the judge if they wanted to notify the Mexican Consulate and if they wanted attorneys, both said yes. Each also wanted to be allowed to call family members.

At 12:45pm, the first suspect, Tijerina, appeared before Judge George Solis. He wore an orange short-sleeve shirt and pants and black flip flops with silver chains around his ankles. His blood-shot eyes bulged in apparent surprise when the judge told him he faced seven different counts.

Tijerina at several points during his arraignment looked around the room and stared at each person, including this reporter and two others, and the county sheriff.

When the charges were being read, Tejerina interrupted to say there was no robbery. Sources told FoxNews.com Tejerina is the one believed to allegedly have fired the shots that killed Vega.

As he was being walked out, he asked if he could have a Bible from the library shelf. He was told he would be brought one later in his cell.

After Tijerina had been escorted out of the small room, Hernandez, thin and lanky and wearing dark green prison garb, was brought in about 1:10pm. He was more vocal than the first suspect. When told of the seven charges he was facing, Hernandez exclaimed "seven charges?" in Spanish.

"I don't understand why I'm being accused of so many things," he told the judge.

Hernandez said he tested negative for gunshot powder. Sources said this suspect’s job in the robbery-turned-murder was to drive the car they planned to steal.

Hernandez said he wanted to tell his wife and his brothers "who live here" what had happened.

"I wish I could let my wife know and my brothers, the ones who are here," he said.

When he was told a lawyer would be provided if he couldn't afford one, Hernandez said, "Yo no tengo dinero. No tengo nada." ("I don't have money, I don't have anything.")

According to court records, Tijerina, who also goes by the name Tijerina-Sandoval, pleaded guilty to entering the U.S. illegally on July 9, 2007. He was given a 30-day sentence with credit for time served and charged a $10 fee.

Three months later, on Oct. 4, he was again found guilty of entering the country illegally and was sentenced to 60 days in jail and $10 fee. In a criminal complaint, he said he entered the U.S. on Sept. 1 and was encountered by border patrol agents near Weslaco, Texas, on Oct. 3. He had waded across the Rio Grande River near Progreso, Mexico, court records show.

A year later, on Oct. 25, 2008, he again crossed into the U.S. by wading across the river. On Nov. 18, 2008, he was given 90 days in jail and another $10 special assessment fee.

On Dec. 15, 2009, Tijerina was indicted by a grand jury on charges of entering the U.S. illegally yet again. The indictment says he "had previously been denied admission, excluded, deported and removed, knowing and unlawfully was present in the United States having been found near Edinburg, Texas." Court records say he had not obtained consent from the U.S. attorney general and the secretary of homeland security to reapply for admission into the U.S.

A warrant issued for his arrest said he faced up to 20 years in prison and a fine of up to $250,000.

He was held without bond on Jan. 26, 2010. He was given nine months in jail and fined $100.

Sources confirmed that these court cases involved the same Tijerina in custody for killing the Border Patrol agent. They said Hernandez, the other suspect, has been deported twice for entering the U.S. illegally.