Any Thoughts on Duplicate Content?

I have a site of my own focussed on social care and I’ve built a site for a couple of Psychologists.

So that I could generate a couple of intelligent back-links for the psychology site I asked for a guest post from one of the psychologists. The post is quite good; topical, interesting and relevant for me but also the same for their site so I have posted it on both.

So does this equate to a problem with duplicate content and will that undo any benefit from generating the back-links? They are both pretty (very) low-traffic.

Thanks

Martin

PS They are both WP sites which is why I have posted on the WordPress board - I couldn’t find a dedicated SEO section.