Summary: This paper deals with the study of existence conditions as well as the construction of eigenfunctions of strongly coupled parabolic boundary value partial differential systems
where lies in and , , and are matrices in . It is an extension of [L. Jódar, E. Navarro and J. A. Martin, Proc. Edinb. Math. Soc., II. Ser. 43, No. 2, 269-293 (2000; Zbl 0949.35033)].