In this contribution the first search at HERA for Odderon induced reactions is presented and contrasted with cross section measurements for Pomeron induced processes. The searches are performed in the channels \gamma p \to  \pi ⁰N^*, \gamma p \to  f₂(1270)X and \gamma p\to  a₂X, where N^\ast denotes an excited nucleon state. The rates found are compatible with the background alone, and the upper limits derived therefrom are confronted with the expectations of a specific non-perturbative QCD model. In contrast, to these findings the cross sections for the Pomeron mediated processes --- \gamma p \to \omega p and \gamma p \to  \omega \pi ⁰ X --- were found to be in perfect agreement with earlier measurements and the expectations from Regge theory with soft Pomeron exchange. The mean \gamma p centre-of-mass energies were \langle W \rangle = 200 GeV and 215 GeV, respectively.

PACS numbers: 11.55.Jy, 13.60.Le