LIFE.com has a great photo slide show that showcases the hotly competitive auditioning process that would eventually name the successor to Sean Connery’s James Bond.

Who Would Be James Bond?
In the early ’60s, movie producers adapting Ian Fleming’s novels about a suave British spy named James Bond plucked a relative unknown, Sean Connery, out of obscurity and offered him the role of a lifetime. And when Connery left the franchise after five movies, the hunt for Bond was on again. LIFE sent photographer Loomis Dean to the final casting sessions for On Her Majesty’s Secret Service (released 40 years ago this week), and the magazine published a handful of those photos. But some of the choicest frames – Bond wannabes suiting up, holding guns, drinking martinis, wooing women – have never been seen