OK, this is weird. I have a new Cecile Brunner that is planted in my garden. It is probably about a year old, but I received it about 6 weeks ago. As soon as I planted it, it was promptly eaten down to the ground by a nasty rabbit. Wouldn't you know, that rose grew like a weed, and now it has the teeniest little bloom on it. Anyway, I went out today to look at the bloom, and it has what appears to be another bud forming -- in the center of the existing bloom! I've never seen anything like this. Never had this type of rose before (actually I'm pretty new to roses in general) so I don't know if this is normal, or what it is.
It's a phenomenon called "proliferation". It is harmless to your rose and tends to occur more with certain varieties.
'Bloomfield Abundance' often does this and is sold in place of 'Mlle Cecile Brunner' at garden centers. The true plant is a miniature, not producing large sprays of flowers with often foliaceous (leaf-like) sepals. http://images.google.com/images?hl=en&ie=ISO-8859-1&q="bloomfield+abundance"&um=1&sa=N&tab=wi
Thanks for the great information! Mine is a miniature -- and it had better be the real deal!! I bought it from a place that guarantees the authenticity of their varieties, and it wasn't exactly cheap.