The pair are both in the running for the 'Music Radio Personality of the Year' and 'Best Entertainment Programme' awards. Skinner and Moyles both won silver awards last year.
The Absolute Radio DJ also has a third nomination in the 'Speech Radio Personality of the Year' category, but Moyles, who set a broadcasting world record for Comic Relief earlier this month, has not received a nomination for his BBC Radio 1 breakfast show in its respective category.
The BBC Radio 5 Live breakfast team, LBC's Nick Ferrari, Talksport's Alan Brazil, BBC Radio 2's Chris Evans and Christian O'Connell from Absolute Radio are, however, nominated in the category 'Breakfast Show of the Year' for shows with 10 million listeners or more.
Radio 5 Live's Victoria Derbyshire is up for three categories - 'Best News and Current Affairs Programme', 'Speech Broadcaster of the Year' and 'Best Speech Programme'.
BBC 6 Music's Jarvis Cocker receives a pair of nominations, for 'Music Radio Personality of the Year' and 'Best Specialist Music Programme'. The Pulp frontman won the Rising Star award for radio newcomers at last year's ceremony.
BBC Radio 3, BBC Radio 4 and Talksport will also fight to be crowned 'UK Station of the Year' at the annual awards, which take place on May 9 at the Grosvenor House Hotel.