Colorado Springs, Colorado (CNN) At the Koch network's summer meeting, top officials repeatedly underscored that their work is part of a movement far bigger than their founder and figurehead.

The subtext: The network established 15 years ago by billionaire Charles Koch is beginning to envision a future without him.

The idea of a Koch-less Koch network is becoming increasingly tangible and, for the network's leaders, undeniable. The moment comes as the Koch network begins to rethink its approach to GOP politics and also finds itself at odds with the head of the Republican Party , President Donald Trump.

The network was until recently colloquially known simply as the "Koch brothers," a reference to brothers Charles and David Koch. But David Koch, 78, stepped down from his role with the network earlier this year due to declining health, and network leaders this weekend counseled reporters to avoid using the term "Koch brothers" in regard to the network.

"It's unfair to (David) and his family to say he had anything to do with it since he's been in declining health," said network co-chair Mark Holden.

David Koch was a later addition to the network founded by his older brother and focused his energies more narrowly on Americans For Prosperity, the network's political arm. Charles Koch has also been the more visible Koch brother as the public face and voice of the network, and the network's leaders played up his vigor and continued commitment.

"There's only one Charles Koch," said James Davis, a spokesperson for the network, "but fortunately he's going really strong."

Nevertheless, David Koch's departure has added some urgency to the question of continuity for the network, which has grown to become a powerful force in politics and policymaking. Meanwhile, the network's leaders recognize that Charles Koch, now 82, will not lead the network indefinitely, and have been gradually laying the groundwork for the network's next phase and priming their backers for it.

Network co-chair Brian Hooks, a key Koch deputy, has become a visible and vocal presence at the network's meetings. At a welcome reception Saturday evening on a lawn at the luxe Broadmoor Hotel, Hooks drew laughs from donors when he recounted a recent hike with Charles Koch, who "beat me up the mountain by a long shot."

Meanwhile, Charles Koch's son, Chase Koch, is being groomed behind the scenes to take on a bigger role and is now heading up the network's New Leaders program, which seeks to recruit a younger generation of business leaders to the network. Roughly 80 donors from the New Leaders program attended the network's summer meeting, organizers said. Meanwhile, Chase's wife, Annie Koch, addressed the network's backers Monday concerning her work launching a private school in Wichita.

That emerging next generation, coupled with Charles Koch's efforts to cement the guiding principles of the network, have given confidence to the network's backers that it will endure beyond its founder.

"Charles has been a great leader, inspiring leader, innovative leader, and helped coalesce this as an organized group," said Art Pope, a donor who hails from North Carolina, "... but as a great leader, it's going to continue beyond him."

Koch "believes in empowering people, he believes in encouraging people to be innovative on their own," Pope added. "So that is a very good operational philosophy. It's not going to rise or fall with one individual or two individuals."

John DeBlasio, a Chicago-based donor, said the network has not taken steps to explicitly reassure donors about its post-Koch direction. But Charles Koch "has given very clear guidance on what he believes and the framework to stay within," DeBlasio said.

Taking questions from reporters on Sunday, Charles Koch didn't directly respond when he was asked about the future of his network and his role in it. "We're going to continue to innovate, learn, correct our mistakes," he said. "All humans are fallible, and we're certainly right there in the lead."

But, speaking to donors Saturday evening, Koch also trumpeted his network's progress over the past five years, which he said was "more progress ... than I've made in the previous 50 (years)."

"We're just getting started," Koch added, "because we have more opportunities in front of us than I ever imagined."