  We define two-dimensional Dirichlet spectrum (with respect to Euclidean norm)
as
  D_2=\lambda\in\mathbf{R} | \exists \mathbf{v}=(v_1,v_2)\in \mathbf {R}^2:
\limsup\limits_{t\rightarrow\infty} {t\cdot\psi_{v}^2(t)}=\lambda, where
\psi_{v}(t)=\min\limits_{1\leqslant q\leqslant t}\sqrt{|q v_1|^2+|q v_2|^2} is
the two-dimensional "irrationality measure function". Our main result states
the equality
  D_2=[0; 2/sqrt{3}].
