The .577 Ty was built on a P14 Enfield by A-Square.

The .585 Nyati was designed to fit in a Model 98 Mauser (after radical alteration) by Ross Seyfried.

A person using the handle Robgunbuilder at www.accuratereloading.com has figured out how to build a .585 Nyati on a CZ550 and make it feed correclty.

However, for either cartridge you are better off getting a Granite Mountain Arms magnum mauser action with .750" bolt body diameter.