As a result of frequent personnel changes, Kukulski disbanded the group in 1972 in order to focus on his wife's solo career.

[2] In the 1970s, he was responsible for most of Anna Jantar's greatest successes and wrote for her notable hits such as, Najtrudniejszy pierwszy krok ('The Most Difficult First Step'), Tyle słońca w całym mieście ('So Much Sun in the Whole City') and Moje jedyne marzenie ('My Only Dream').

After Anna Jantar's death on 1980, he continued to compose songs for his daughter Natalia and many other famous Polish artists such as Irena Jarocka, Eleni Tzoka, Krzysztof Krawczyk, Anna German, Felicjan Andrzejczak, Bogusław Mec and his second wife Monika Borys.

He served as composer from Polish films Nie zaznasz spokoju (1977), Komedianci z wczorajszej ulicy (1986) and Pan Samochodzik i niesamowity dwór (1987).

At the end of the 1990s, TVP Polonia broadcast a regular program devoted to the work of outstanding Polish artists, mainly composers and authors of texts entitled "Z archiwum i pamięci" ('From the Archive and Memory').

For his services to Polish music, President of Poland Aleksander Kwaśniewski awarded Kukulski the Knight's Cross of the Order of Polonia Restituta.