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 victorious 4×100 m relay team. At the Tokyo Olympics two years later she finished second in both events. She was also good in freestyle swimming, a fact 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 gold in the 200 m butterfly in a time of 2:24.7, beating East German Helga Lindner by 0.1 seconds. The 100 m in Mexico ended in disappointment for her. She did not feel well physically and only came fourth.
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 m 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 zip 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 metres I was in the lead. Twenty metres from the finish I saw someone (Lindner) catching up with me. I thought: Jesus, no, she's not getting past me. Fortunately I was able to keep in front'.
In her memoirs recorded by Henk Lichtenveldt she said:
Approaching the podium of honour 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.