According to witnesses, the second bomb killed at least 40 people.
(READ MORE: At least 13 killed in bombing of Nigeria World Cup viewing venue)
Casualties from the first blast could not immediately be ascertained and Nigerian security sources could not immediately be reached for comment.
Bomb blasts that bore the hallmarks of Islamist Boko Haram militants killed 118 people in the same area of Jos in May.
"I saw a flash of light and heard a loud boom. Afterwards there was debris everywhere and mutilated bodies," witness Tanko Mohammed said of the blast in Jos's commercial Terminus district. A Reuters reporter counted 11 bodies at one bomb site and 29 at the other.
Boko Haram is a Sunni jihadist movement that has been waging a five-year insurgency to establish an Islamist state in the northeast of the country.
(READ MORE: Bombings kill at least 118 in central Nigerian city of Jos)
President Goodluck Jonathan declared a state of emergency in three northeastern states last year. The number of attacks has risen sharply since then, in the run-up to elections in February 2015.
The latest blasts came as both Jonathan's ruling party and the main opposition coalition agreed on candidates to contest the elections, in which security is likely to be a major campaign issue. Former military ruler Muhammadu Buhari will be challenging Jonathan at the polls for the second time.