Answer: Some peach and apricot trees ooze an excessive amount of sap, which can fall or flow onto ripening fruit. The sap is usually associated with brown rot disease, or insects which bore into the branches, causing injury. Inspect your tree carefully, looking for round holes, or cracks and fissures in the bark. If none are found, I suspect the excessive sap is natural for your tree and is travelling down the stem of the fruit where it's attached to the branch.
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