Before coming to St. Louis in 1996, Vonk held a succession of posts in Europe, serving simultaneously as the chief conductor of the Dresden Staatskapelle Orchestra and the Dresden State Opera in the 1980s, and leading the Cologne Radio Symphony in the 1990s.
Vonk began to experience weakness in his hands and feet in the summer of 2001, and was initially diagnosed with a relapse of Guillain-Barré Syndrome, from which he had suffered in 1988. But the condition worsened in February 2002: during one concert, he had to be helped from the podium, unable to continue, and he canceled a series of appearances.
Eventually it was determined that Vonk had a disease similar to amyotrophic lateral sclerosis (ALS or Lou Gehrig's disease), but so rare that it does not have a name. In April 2002, he announced that he would step down as music director. He gave two final performances in May, leading Mahler's Fourth Symphony for emotional audiences. Asked to speak after the second concert, he characteristically declined, saying that he had said everything he needed to in the music.
The son of a violinist, Vonk studied law before transferring to the Amsterdam Conservatory. In 1966, he was appointed conductor and rehearsal pianist of the Netherlands Ballet and eventually married ballerina Jessie Folkerts. In the 1970s, he was an assistant conductor of Amsterdam's Concertgebouw Orchestra before becoming chief conductor of the Netherlands Opera. He also held positions with the Netherlands Radio Philharmonic, Royal Philharmonic Orchestra, and the Residentie Orchestra of the Hague.
A frequent guest conductor with orchestras and opera houses around the world, Vonk made his first appearance in St. Louis in 1992. According to the St. Louis Post-Dispatch, he brought discipline and "clarity of tone" to the orchestra.
After Vonk's unexpected departure, violinist and conductor Itzhak Perlman agreed to help guide the SLSO as music advisor; in December 2003, the young American David Robertson was named as Vonk's successor, starting with the 2005-06 season.