Most of the assaults happened between 11.30pm and 1.30am in Marktplatz, when the noise and excitement was at a peak.
A further four women have reported that they were sexually assaulted during New Year's Eve celebrations in the city of Salzburg.
It's increasingly common for these activities to include the exchange of pictures or motion video.
There are companies which allow paying customers to actually watch people have live sex or masturbate and at the same time allow themselves to be watched as well.
Two women who were harassed took photos of two of the men with their mobile phones, however the quality of the photos is not very good as it was already very dark outside.
Police said that they questioned all the victims on New Year's Day, before they returned home.
A police spokesman said it's likely that it was one group of men who harassed the various women, and that the men “had a system”.