In 1983 he became soloist of the Slovak National Theatre and participated in projects in Germany, Spain, Switzerland and Russia.
He cooperated with many renowned conductors such as Bruno Bartoletti, Riccardo Muti, Wolfgang Sawallisch, Peter Schreier, Fabio Luisi, Christian Thielemann and others.
He also performed in Beethoven's Missa Solemnis in Graz and in Shostakovich's De la poésie Juive in Paris.
In other seasons he took part in concerts on many European stages with Dvořák's choral works and Verdi's Requiem.
Kundlák performs a large Mozart and Haydn repertoire and concert works by Dvořák, Janáček, and Stravinsky.