Tom Wopat is admitting he has a substance abuse problem on the heels of his arrest for indecent assault and cocaine possession.

The former "Dukes of Hazzard" star's rep released a statement, saying he's "taking personal time to address his ongoing struggle with substance abuse. While death and illness in the family, combined with the intensity of his recent schedule, certainly contributed to his misstep, Tom definitely understands that sobriety is the sole course for a successful future."

Wopat pled not guilty to the felony assault charge last week. TMZ broke the story ... he's accused of groping a woman's butt and putting his finger in between her butt cheeks. The alleged assault happened on the set of a stage production of "42nd Street" ... in which Tom was supposed to star.

His rep said Tom hopes his "good name will be restored" once an investigation is completed.