On Mon, 5 Sep 2011 11:28:25 -0700 (PDT), Higgs Boson
wrote:

I put in two very young fruit trees about 4-5 months ago. Both are
doing well. However, there are suckers appearing from the bases. At
least I THINK that's what they are.

Any advice on what to do?

Should be obvious, any shoots below the graft should be nipped off...
above the graft is at your descretion, depends on how you want the
tree to grow... some prefer multi-trunked fruit trees. What kind of
fruit trees?