Let \(A_0A_1A_2A_3\) and \(B_0B_1B_2B_3\) be any two nondegenerate tetrahedra in the three-dimensional projective space \(P_3(F)\) over a field \(F\), which are situated in such a way that \(B_i\in\alpha_i\), \(B_i\not\in\alpha_j\) for \(i\neq j\) \((i,j= 0,1,2,3)\) and \(A_i\in\beta_i\) for \(i= 0,1,2\), where \(\alpha_i(\beta_i)\) is the plane determined by the set of points \(\{A_0,A_1,A_2,A_3\}\backslash \{A_i\}\) \((\{B_0,B_1, B_2,B_3\}\backslash \{B_i\})\). The author now proves the theorem: Under these assumptions \(A_3\in\beta_3\) is valid in \(P_3(F)\) (``Theorem of Möbius'') if and only if the field \(F\) is commutative.