The Alexander brothers each got 30 years in federal prison for sex trafficking … but, according to their rep, the disgraced real estate moguls’ “lives are not over” and they’re only beginning their fight to clear their names.

The brothers’ rep, Juda Engelmayer, tells TMZ … not only are their lives not over … but neither is the case because Juda says “serious questions remain about the fairness of the proceedings, and they intend to pursue every available avenue of appeal.”

As you know, Oren, Alon, and Tal Alexander appeared Tuesday in Manhattan Federal Court, where a judge handed down the harsh punishments to them.

All three brothers were found guilty in March on 10 counts of conspiracy to commit sex trafficking and sex trafficking by force. Prosecutors said the brothers drugged and raped women going back to their high school days in the early 2000s.

Eleven women testified they were sexually assaulted by the brothers and they gave victim impact statements at yesterday’s sentencing hearing. More than 60 women came forward to tell prosecutors about their nightmarish interactions with the brothers.

Despite this, Engelmayer says “thirty years is an extraordinarily severe sentence, and the Alexander family is devastated, but the brothers are not giving up, and neither are their loved ones.”

Engelmayer also says that although the brothers recognize the difficult road ahead, they continue to maintain their innocence and intend to fight their convictions. Engelmayer noted the brothers acknowledged in court that “they behaved in ways they deeply regret, particularly in their treatment of women.”