Vasiukov was unable to maintain his peak of the early 1960s, but he remained remarkably competitive for many years afterwards, especially in international tournaments outside the Soviet Union which had mixed-strength fields, where he scored most of his successes. He won several titles, and was almost always around the top places, when he competed outside the Soviet Union. He tied for first at Polanica Zdroj 1965 with Peter Dely at 9½/13. At Reykjavík 1968, he tied for first with Taimanov on 10½/14. He again tied with Taimanov for the title at Skopje 1970 with 11/15. Vasiukov claimed his fifth Moscow Championship in 1972.