<p>In this paper, we study the property of hereditary completeness of vector systems <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{x_k\}_{k=1}^\infty\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mo stretchy="false">{</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo stretchy="false">}</mo> </mrow> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>∞</mi> </msubsup> </math></EquationSource> </InlineEquation> in a Hilbert space. A criterion of hereditary completeness is obtained in terms of projectors on closed linear spans of systems of the form <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\{x_k\}_{k \in N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mo stretchy="false">{</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo stretchy="false">}</mo> </mrow> <mrow> <mi>k</mi> <mo>∈</mo> <mi>N</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(N \subset \mathbb {N}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>⊂</mo> <mi mathvariant="double-struck">N</mi> </mrow> </math></EquationSource> </InlineEquation>. Developed technique has been used to prove that mixed systems of a hereditarily complete system are also hereditarily complete. In conclusion, the problem of possible defects in a nonhereditarily complete system is considered.</p>