A number of statements on fundamental matrix of solutions of the Cauchy problem for $\vec{2b}$-parabolic systems with degeneration on the initial hyperplane is established. The statements are related mainly with properties of fundamental matrix of solutions as a function of time variable.

[1] Berezan L. P., Ivasyshen S. D. Fundamental matrix of solutions of the Cauchy problem for $\vec{2b}$-parabolic systems with degeneration on the initial hyperplane // Supplement of the NAS of Ukraine. – 1998. – No. 12. – P.7–12.

[2] Berezan L. P., Ivasyshen S. D. On strongly degenerate on the initial hyperplane $\vec{2b}$-parabolic systems // Bulletin of the State University "Lviv Polytechnic". Applied Mathematics. No. 337. – Lviv: Publishing House of the State University "Lviv Polytechnic", 1998. – P.73–76.

[3] Berezan L. P. Integral representation of solutions of the generalized Cauchy problem for a strongly degenerate on the initial hyperplane $\vec{2b}$-parabolic system // Nauk. visnyk Chernivtsi Univ.: Zb. nauk. pr. Vys. 46. Mathematics. – Chernivtsi: ChDU, 1999. – P.13–18.

[4] Medinsky I. P. On the properties of the fundamental matrix of solutions of the Cauchy problem for a parabolic system with degeneracy on the initial hyperplane // Visnyk State Univ. "Lviv Polytechnic". N364. Applied mathematics. – Lviv: Publishing House State Univ. "Lviv Polytechnic", 1999. – P.298–307.

[5] Ivasishen S.D., Eidelman S.D. $\vec{2b}$-parabolic systems // Proceedings of the seminar on functional analysis. -K.: Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR. - 1968. - Issue 1. - P. 3-175, 271-273.

[6] Voznyak O.G., Ivasyshen S.D. Fundamental matrices of solutions of parabolic systems with degeneration on the initial hyperplane. - Chernivtsi. unt. - Chernivtsi, 1995. - 51 p. - Dep. in DNTB of Ukraine 07.95, N1808-Uk95.