you can find your answer in this book: food nutrition and diet thrapy ( krauses), mahan

There have been numerous recommendations for dietary treatment of autism, suggesting that eliminating dairy, gluten, food additives, or various allergens. Some of these things may help some kids with autism, but for the most part, the nutritional needs are the same as for any child of the same age, unless a specific food sensitivity is clearly identified.

To the best of my knowledge there are no dietary inclusions or restrictions that apply to all children with either of these diagnoses.

Down Syndrome: There is a risk of obesity over time, so healthy eating related behaviours, along with lifestyle (exercise, sleep) are important to establish and habituate.

Autism: there are a wide range of individual needs within this heterogeneous diagnosis. Each child is somewhat of an experiment. It is likely that some children have GIT related symptoms, possibly biome related, but there is no real science at this time that I believe is better than intelligently constructed trial and error. Food related problems are more likely of the child has GIT symptoms such as bloating, constipation or diarrhoea.

A related problem is hypersensitivities (smell, taste, texture) - fussy eaters may need professional guidance to avoid nutritional deficiencies.

I thank you for all who respond to my question.

It is common for Down Syndrome infants to have cardiac defects (AVSD, PDA), which may result in fluid restrictions or problems with feeding. This should be taken into consideration as it can affect their nutritional requirements.

There is a high frequency of underactive basal metabolism among individuals with Down syndrome. It may be worth screening for this or certainly investigating this if their are any possible symptoms. If found, it should be treated but since it is not universal, it should not always be assumed to be present.

Might be worth looking at the GAPS nutritional protocol http://www.gaps.me/

I'm hoping to conduct an observational study of its effectiveness soon, as it appears to be helpful.

Children with both Down syndrome and autism ussually have sensory integration problems. This cause depending on extend difficulty in feeding/eating.  Together with low muscle tone around the mouth and swallowing this can become really complicated. Look at work of Prof Winnie Dunn an Occupational Therapist and the profiles availble to test for the extend and patern of Sensory Integration (SI).  I my experience as a dietitian both mom and child needs lots of support around their eating.  The poor mom is often seen as the reason for the eating problems. Of the problems can be that the do not eat at other peoples houses, do not eat "mixed" food, do not like pieces or lumps in food, do not like the food to touch each other on the plate to name a few.

I make use of the chaining principal to see what child is eating and help to expand on that. I am very careful to exclude foods out of the diet unless their is positive reasons for food allergy - these children are also more often allergic.

Diet silencing reactivity of the immune system and digestive tract:

lactose-free, gluten-free, sugar-free, low salicylate, low GI, without additives foods. However, the choice of the diet should be individually matched to the child

They know if there fibles studies on nutritional intervention in children with Down syndrome ?