The paper discusses the possibility of use of nanocomposites obtained by laser structuring of single-walled (SWCNTs) and multi-walled (MWCNTs) carbon nanotubes in bovine serum albumin matrix as tissue-engineering scaffolds for blood vessel network sprouting in the process of biodegradation of the nanocomposite implant. The lowest rate of biodegradation was obtained in bulk and film nanocomposites based on SWCNTs immersed in NaCl solution: 2.45 and 9.77% weight loss after 14 days, respectively. Analysis of the dynamics of changes in the optical density of NaCl solution showed intense biodegradation of nanocomposites after six days of immersion. Spectral studies showed that contact of blood with bulk and film nanocomposites based on SWCNTs did not lead to hemolysis (hemolysis level ≤ 0.5%).