The flags were flown from the mainmasts at the sites from morning colours at 08:00 until evening sunset, and both flags will remain flying until Sunday to mark Pride Week.
The flags have six colours which represent: red for life, orange for healing, green for nature, indigo for serenity and violet for spirit.
Military and civilian personnel gathered at both sites to witness the events, with representatives from diversity and inclusion organisations including the HMNB Clyde Equality Diversity and Inclusion Committee, Pride in Babcock and the Royal Navy Compass Network.
HMNB Clyde's Equality Diversity and Inclusion Committee aims to ensure the workplace at Clyde allows everyone to realise their potential and to ensure it is a community everyone feels a part of and is proud to belong to.
The committee includes members from various departments across the base, including the Ministry of Defence (MOD), Royal Navy and Babcock.
Kerry Brabender, Business Department People Team and chair of the committee, said: "I'm delighted that we are able to fly the rainbow flag at both sites again this year.
"It's important that the Clyde Community comes together to celebrate Pride, to show support to the LGBTQ+ community and champion the inclusion of all staff, ensuring that we create a workplace where all staff feel supported to bring their true selves to work."
Hamish Fowler, Babcock's Fleet Operations Director at HMNB Clyde and board sponsor for diversity and inclusion, said: "I'm delighted to be present today as the Pride flag is hoisted above Faslane.
"Supporting diversity in the workplace is a priority for Babcock. Having the opportunity to join the flag-raising today, as a member of the HMNB Clyde community, is a great way for us to re-affirm our goal to become a more diverse company."
The Royal Navy Compass Network is the Sexual Orientation and Gender Identity Network of the Naval Service.
It aims to provide an inclusive Naval Service in which people feel comfortable, valued and empowered to be themselves and express their sexual orientation and gender identity, realise their career potential and contribute fully to the service.
The original pride flag, which was devised by Gilbert Baker, who served in the US Army, first flew at the San Francisco Gay Freedom Day Parade on 25 June 1978 and had eight stripes.
Cover image: Rainbow Flag is raised at HMNB Clyde to mark Pride Week (Picture: MOD).