Let c: \(S^ 1\to {\mathbb{R}}^ 3\) be a smooth curve, P an affine plane in \({\mathbb{R}}^ 3\). The total order of contact of P to c is the sum of orders of contact of P to c at all contact points. Let A(2,3) be the set of affine planes in \(R^ 3\), and \(A_ r\) the subset consisting of those planes whose total order of contact to c is equal to r. For c in general position, the \(A_ r's\) with \(r>3\) are empty, and \(A_ 3\) is a finite set. Each \(P\in A_ 3\) is called a triple tangency. A triple tangency is called a T-plane, C-plane and I-plane according as the number of tangent points is equal to 3, 2, or 1. The author shows that under additional assumptions the number of C-planes is even.