"Secret space program" is a term generally used in conspiracy theories and fiction, not for a publicly acknowledged government or scientific endeavor on the scale implied by the theories. 

However, the U.S. and other nations do operate highly classified military and intelligence space missions with undisclosed payloads and objectives. The existence of these specific missions is not entirely hidden, as launches are trackable, but their specific operations and technologies are kept secret for national security reasons. 

Yes. The United States Secret Space Program is Still Very Active

Classified Military Space Activities

Classified Missions: The U.S. Space Force and the National Reconnaissance Office (NRO) regularly launch classified payloads into orbit. While the launches themselves are public knowledge (due to the impossibility of hiding a rocket launch), the exact purpose, capabilities, and detailed operations of the spacecraft are classified.

X-37B Spaceplane: A notable example is the uncrewed X-37B, a reusable military spaceplane that has flown multiple long-duration missions for the U.S. Space Force. Officials have revealed it tests advanced space technologies, but most of its specific experiments and operational details remain a government secret.

Declassification Efforts: Recently, the Pentagon has moved to declassify some highly sensitive space programs and technologies, aiming to boost the nation's military edge by sharing more information with allies and within the Defense Department. 

Conspiracy Theories and Fiction

The popular concept of a "secret space program" with bases on the Moon and Mars, often involving extraterrestrial alliances or advanced anti-gravity spacecraft, originates largely from fiction and conspiracy theories. 

Origins: The idea was notably popularized by a 1970s British spoof documentary called Alternative 3, intended as an April Fool's joke, which has since grown into a widespread myth.

Whistleblowers and Authors: Personalities in the "disclosure movement," such as Corey Goode and Michael Salla, have written books and given testimonies claiming to be whistleblowers or insiders of these programs, but their claims lack verifiable evidence and are considered fiction within the scientific and government communities. 

In summary, while national militaries have highly secretive, classified space missions, the "secret space program" as described in popular conspiracy theories is a separate, fictional concept.