We classify invertible 2-dimensional framed and r-spin topological field theories by computing the homotopy groups and the k-invariant of the corresponding bordism categories. By a recent result of Kreck, Stolz and Teichner the first homotopy groups are given by the so called SKK groups. We compute them explicitly using the combinatorial model of framed and r-spin surfaces of Novak, Runkel and myself.