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Bottle feeding kittens on your own is a demanding task. You will need to feed the kittens every 1-2 hours around the clock for the first week of their life. This is necessary to give the kittens the best chance of survival. Don’t be afraid to ask for help from your veterinarian or local animal shelter. They may be able to provide a surrogate mother cat or connect you with volunteers who have experience with bottle feeding newborn kittens. Some organizations may even be able to provide you with free supplies to help you care for the kittens. A young kitten can only digest milk from the mother-cat. If the mother cat has abandoned her kittens, you will need to feed the kittens a cat-milk replacement. Cow's milk is not suitable because it contains lactose which many cats cannot digest and it will give them diarrhea. In an emergency situation, goat's milk is unlikely to cause harm and will stop a newborn from getting dehydrated.  Cat-milk replacement formula is available via the internet or from your local veterinarian. These formulas are an exact replica of the balance of fats, proteins and vitamins found in a queen's milk. They come in powdered form and are reconstituted with boiled water, in much the same way that human milk replacers are. Always make each feed up fresh prior to use, since the high fat content encourages bacterial growth and quickly becomes contaminated. Make sure the kitten is warm – a chilled kitten will not be able to digest milk which will then curdle in her stomach and make her ill. Make up sufficient milk replacement for that feed and place it in a clean, sterilized feeding bottle. Special feeders for premature kittens are available, which have the advantage of being a convenient small size so they are easy to use with tiny kittens and don't waste milk. A premature kitten has a lot in common with a cold-blooded animal – if the room is chilly she cannot generate a high enough temperature for the enzymes of digestion to work. Place the kitten on her belly, in a similar way that she would suckle from the mother. It can help the kitten to find the teat if you first put a drop of milk on the tip and touch it to her lips. If the kitten still will not suckle, try stroking its head and back to encourage it to feed. When the kitten starts to make a sucking noise, try to offer the nipple again. Allow her to suckle until her belly is nicely rounded, but not bloated and tight. You can check this by feeling to see if her tummy is wider than her ribcage – if it is then her stomach is full and she has had sufficient feed for now. Many kittens will fall asleep on the teat when their tummy is full. If this happens, gently remove the teat from her mouth and place her back in the warm nest. Kittens need to be burped after a formula feeding, so you will have to do this yourself. To burp a kitten, place it over your shoulder on its stomach and gently pat it on the back. Keep patting until you feel or hear a burp. Make sure that you use a damp towel to clean off any formula that the kitten burps up. Shortly after giving birth, the mother-cat produces special milk called colostrum, which is high in antibodies. These are immune complexes that help to protect the kitten against diseases that the mother has encountered, similar to a vaccination. The colostrum strengthens the kittens and may even improve their chances of survival. Colostrum is also rich in the vitamins and minerals that kittens need for normal growth and development. A strong kitten will latch onto the nipple when placed against it, and start to suck. A weak kitten may need some help. To do this try expressing a drop of milk/colostrum from the nipple, and touch her mouth to the milk so as to get a taste and encourage her to latch on.  The rear teats tend to produce the most milk. When expressing colostrum, chose a rear teat and gently place the fore-finger and thumb of your dominant hand just behind the nipple. With a gentle squeezing-pulling action travel the finger and thumb to towards the teat. Do this repeatedly and oftentimes the dam will release milk. Make sure they feed often. A premature kitten is entirely dependent on her mother's milk for nutrition. She feeds little and often, with a newborn feeding as frequently as every 1-2 hours.
Consider seeking help from your veterinarian or local animal shelter. Get kitten-safe milk if the mother-cat is unavailable. Prep your kittens' environment and food. Position the kitten on her belly if you're feeding her yourself. Burp the kittens after a formula feeding. Make sure the kittens get their mother’s colostrum, if possible. Help each kitten get her mother's milk, if necessary.