See had to go on a search now. I'm a research junkie *l*
Seems the mule Krause that mothered "Blue Moon" and "White Lightening", in Nebraska in the 1980s, was the subject of some study because the donkey sire of both foals was ALSO Krause's sire herself. This was on one website I found:
*Can Mules Reproduce? Or FERTILE MULES? (Mules giving Birth/Mule gives Birth/Mule has a foal) Do they have normal anatomy?
What is the offspring of a horse and a mule called? Can a mule have a baby?
Short answer - No, mules (both male and female) are sterile. Both have normal anatomy internally and externally. The males must be castrated, as they have the equipment but do not produce the essential element needed (we're trying to keep this PG here...) Females may come into heat and may need hormone shots if heat is a problem.
For those who are following up with "Okay, what about the fertile mule we have read about..." - Fertile mules (hinnies) are a 1 in 1 million case occurance. All known fertile hybrids in the equine world have been female mules or hinnies. Why these few is still scientifically a mystery, and there is still scientific debate over the verification of some "Fertile"; cases. The most well known and documented cases are of Krause, a mare mule with two mule sons, and a fertile hinny in China, who;s offspring, Dragon Foal, is considered unique. The complications for Krause's cases is that her sire, Chester, is also the sire of her sons. However, DNA testing has been cataloged as conclusive that both foals, Blue Moon and White Lighting, are Krause's foals.
In most known cases of mule fertility, it has been noted that the mare mule passed on a complete set of her Maternal genes to the foal. Therefore a female mule bred to a horse would produce a 100% horse foal. Thus was the case of Old Beck, who was at Texas A&M in the 1920's;. This mare mule had a mule daughter, Kit. She was brought to TX A&M for observation. She was bred to a saddle horse stallion, and produced a horse son, Pat Murphy Jr. Pat Jr was fertile, and sired horse foals. Beck aborted a third foal, sired by a jack, which although deformed, appeared to be a regular mule.
There has more recently been a case of a mare mule in Brazil who has foaled two 100% horse sons. Tests in the future will hopefully prove them to be normal, fertile stallions.
Dragon Foal, instead of being a donkey foal from the mating of a hinny to a jack, is a unique hybrid, with combinations never documented before. Visually, she appears to be a strange donkey with some more mule-like features, and her chromosomes and DNA test seem to confirm this.
A mare mule in Morocco foaled in 2003 and was genetically confirmed to have been the dam of the male foal. His DNA shows him to be a mixed karyotyped hybrid like Dragon Foal, approximately 3/4 donkey and 1/4 horse.
In the spring of 2007 a mare mule in Colorado gave birth to a live foal. DNA from both the mare mule and her foal has been tested by two different labs to date (July 2007). Both labs have thus verified that the foal qualifies as the offspring of the mare mule, and that she (the mother) is a mule and not a donkey or horse. This is just one more case of mule fertility that will be under investigation. Unlike other cases of fertile mare mules, this foal appears to be a mixture of horse and donkey phenotypes (ie, visually he looks more donkey-like than mule-like at this stage). Study of the gene mapping will show later if he is a true mixture, as in the case of the Moroccan mare mule, or Dragon Foal in China. Krause, the fertile mare mule in Nebraska in the 1980s, contributed a complete maternal gene set to her sons, making them pure mules (not a 3/4 donkey 1/4 horse mixture).
In the feline world, there are hybrids of Jungle cats and domestic cats, crossed by breeders to have a large cat with the wild markings and still be a pet. The first-generation female hybrids (F-1) are fertile, but the males are not. It is not until the F-3 generation (F-1 Crossed back to domestic cat is F-2, F-2 back to domestic cat again is F-#) that the males become fertile again.
There have been no recorded cases of entire male mules (Male mules are always gelded for use and show, no stallion mules are allowed) ever siring a foal. The cases of fertile Mare mules are so low that the F-3 generation has not been documented or verified in order to test this theory. There is one case (which has no scientific backing) of a mare mule whose Mule daughter was also fertile, and foaled a male "hule" (very horselike in appearance but with some mule characteristics) but no testing was ever done on the hule, and it is not known if he was routinely gelded or was left entire.
Basically, donkey x donkey is a donkey. Donkey x horse is a mule. Donkey x horse hybrids, called mules or hinnies, are sterile and cannot have babies.
This was from Frequently Asked Questions