During 1946-1949, he studied musicology at Charles University in Prague and privately orchestration and conducting with Otakar Jeremias. In 1949, he left his native Czechoslovakia and for the next few years (1950-1952) he worked as music program director of the Czechoslovak Section of Radio Free Europe in Munich, Germany. In 1952, Zajicek immigrated to the United States (he became American citizen in 1957). Here he continued his music education with Karel Boleslav Jirak, first privately (1952-1955) and later at Roosevelt University in Chicago (1955-1958). He completed his composition studies under Paul Pisk (1959-1960). From 1964-1996, Zajicek taught composition and conducting at the Loop College, Chicago. In 1998, he received honorary citizenship from the City of Hrochuv Tynec.