The deadliest incident was in the coastal city of Zliten, where a truck bomb exploded outside the school, killing more than 50 people, a security source said.
The attack was the deadliest since the 2011 revolution that toppled longtime ruler Moamer Kadhafi.
A witness in Zliten, about 170 kilometres (100 miles) east of Tripoli, told AFP some 300 men, mainly coast guards, were inside the compound at the time.
Health ministry spokesman Ammar Mohammed Ammar said 50 to 55 people were killed and at least 100 wounded. Victims were rushed to several hospitals and urgent calls were issued for blood donations.
The blast blew out windows and charred concrete buildings inside the compound and turned cars into black and twisted wrecks, reported an AFP correspondent from the scene.
Hours later another bomber drove an explosives-packed car into a checkpoint in a key oil region under recent assault by the Islamic State (IS) group, killing six people, including a baby.
“I am at the morgue where six bodies from the site of the attack were brought, including the body of a child,” said Mansour Ati, the head of Libya’s Red Crescent. Eight people were also wounded.
Ossama al-Hodeiri, a spokesman for the security forces that guard nearby oil facilities, told AFP: “A driver in a Toyota Land Cruiser blew himself up at a checkpoint at the entrance to the town of Ras Lanouf.”
Hodeiri, who was at the scene, aid three guards and a 16-month-baby were among the dead.
There was no immediate claim of responsibility for the attacks in Zliten or Ras Lanouf but IS has claimed previous suicide bombings and other atrocities.
Libya has had rival administrations since August 2014, when an Islamist-backed militia alliance overran Tripoli, forcing the government to take refuge in the east.
The internationally recognised government condemned the attack as a “cowardly terrorist act” and called for the lifting of an arms embargo it says has prevented authorities from tackling IS.
A deputy defence minister for the Tripoli-based government, Mohammad Bashir al-Naas, vowed to revenge.
Hundreds of people braved the cold and high winds Thursday afternoon to attend a prayer service for the victims of the truck bombing at Zliten’s stadium.