Her international career started in 1962 when, at the age of fifteen, she took the European title in the 100 m butterfly in Leipzig. She was also part of the silver 4×100 m medley relay team. At the Tokyo Olympics two years later she finished second in both events. She was also good at freestyle swimming, which showed when she took second place in the 400 metres at the 1966 European Championships in Utrecht. In the same tournament she also won the 100 m butterfly and the 4×100 m relay. She achieved nine world records between 1963 and 1967 in the 100 m and 200 m (not introduced until later).
Kok reached her peak at the 1968 Summer Olympics in Mexico City. She won the gold medal in the 200 meter butterfly race in a time of 2:24.7, beating the East German Helga Lindner by 0.1 seconds. The 100 meter butterfly race in that Olympic Games ended in disappointment for her, when she did not feel well beforehand, and finished in fourth place..
|“||Normally after a race there were always people around me. This time nobody. Nobody. I suddenly felt so abandoned and alone. Then under the shower I lost control and cried my eyes out.'|
For the 200 meter final, I was so stiff and rigid that I couldn't even see myself getting my tracksuit bottoms off. My fingers couldn't get the zipper undone. An official had to help me with it. I don't remember anything now of the first hundred metres. It's a black hole. Well anyway, after 150 meters I was in the lead. Twenty meters from the finish, I saw someone (Lindner) catching up with me. I thought, "Jesus, no, she is not getting past me." Fortunately, I was able to keep in front.
In her memoirs written by Henk Lichtenveldt, she stated:
|“||Approaching the podium of honor I felt like I was walking on clouds. I had to contain myself because I wanted to rush over the stands skipping like a foal. This was the crowning moment in a great swimming career.|