Duggar Son Allegedly Admitted to Sexually Molesting Minor Girls, Including Sisters

Josh Duggar, one of the members of the family that stars in TLC's "19 Kids and Counting" ... was the subject of a police investigation for allegedly sexually molesting 5 girls, some of whom are his sisters.

The story was broken by In Touch Weekly, but TMZ has confirmed with law enforcement that Josh Duggar -- who was around 14 at the time -- was the alleged molester against 5 girls starting in 2002.

According to the police report, Josh fondled the genitals and breasts of the girls, some of whom were sleeping, but sometimes they were interacting with him ... in one case reading a book.

There was another reported incident 9 months later. According to the police report, the police were not immediately contacted. Instead, Jim Bob, the dad, met with church elders and agreed Josh should be put in a treatment program. The police report says Josh's mom, Michelle, said it wasn't really a treatment center ... they simply sent Josh to a guy who was remodeling a building to do manual labor.

In 2006, the family was scheduled to appear on "Oprah," and before the show someone sent an email to Harpo warning that Josh had molested girls. Harpo forwarded the email to a hotline, which triggered a police investigation.

Cops wanted to question Josh, but Jim Bob lawyered him up and Josh declined the invitation.

Josh, who is now 27, apparently cannot be charged because the statute of limitations has run.

As for the Duggars, one of the family members told investigators, "this entire incident had brought the family closer to God" ... this according to the police report.