Alabama, Georgia, Tennessee and Virginia were among the states where both triumphed. Mr Trump was defeated by Ted Cruz in Texas and Oklahoma.
Democratic candidate Bernie Sanders won Oklahoma and his home state of Vermont. Super Tuesday sees 11 states voting on the biggest single day ahead of the 8 November presidential election.
Mrs Clinton has also taken Arkansas and Texas, and Mr Trump has won Massachusetts.
The former secretary of state and real estate mogul entered Super Tuesday as the favourites to win the vast majority of states for their respective parties.
Speaking at a press conference in Florida - where Mr Trump has been campaigning ahead of the state's vote later this month - the billionaire insisted he had "expanded the Republican party", referring to higher turnout from a broad demographic in states that have already voted.
Mr Trump described himself as "unifier" who could put internal fighting in the Republican party behind him to focus on a general election race against Mrs Clinton.
Source - BBC
