Infantile seborrhoeic eczema can be very common, as it is sometimes known as cradle cap, which usually occurs in babies before their first birthday. It's quite common and can start on the scalp and spread, sometimes it may begin as what looks like a severe nappy rash. Our daughter had it and we were reassured by our health visitor it was cradle cap and would disappear within a few months and probably wasn't uncomfortable for our daughter.
Generally this cradle cap clears up within a few months with moisturising and using bath oils. However, there have been cases where it can persist and this could be down to a number of reasons,
serbaceous gland problems (overactivity)
If your child is unlucky enough to have this eczema persist into their infancy then I can only suggest seeking the advice of your doctor/physician. In some cases this eczema can become severe, whereby the skin cracks and starts to bleed, this can increase the risk of infection and the sooner this is limited the better. My daughter spent many periods of her young life on antiobiotics, as a result of infection from eczema induced skin cracks.
This can be worrying especially as I didn't want my daughter to become immune to antiobiotics by overuse, as maybe in later years she may need antiobiotics for some other symptoms and they'll just not work.
I looked at using various oils to ease the cradle cap and found Naim Oil helped stop the dryness, I've heard of other people using Olive oil to Primrose Oil and reporting satisfactory results but I think it's down to trial and error to see what really works. I only used Naim Oil because I was already using it, to massage my scalp once a week and thought maybe I'd give it a go to help with the infantile seborrhoeic eczema.