Cockatiels and budgies are vulnerable to worm-like internal parasites, with the most common being roundworm. 
Aviary birds are a lot more susceptible to worms than cockatiels and budgies housed indoors all the time. This is due to wild birds perching on aviaries and their infected droppings landing on the aviary floor. The floor harbours the parasite eggs and the aviary cockatiels, parakeets and budgies come into contact with these when they graze on the floor.
Indoor Pet Birds can still have worms
Be aware that indoor pet birds can still be infested with worms. If you hang your cockatiel or budgie cage outside at all, wild birds will occasionally sit on top of the cage, with possible contamination from their droppings. Your pet bird may have contracted worms from the aviary or pet store you obtained the bird from. And, be careful when you introduce a new cockatiel or budgie to your existing bird as it may be a carrier of such disease.
Protection from worms
Hygiene is the key. You must maintain a strict cleaning regime, with regular and thorough cleaning. Aviary birds should be treated for worms on a regular basis. An aviary with a natural environment – greenery and dirt floors – is prone to a build up of parasites, so requires more attention to cleanliness and regular worming of the birds.
Keep seed and water dishes free of droppings – do not place them under perching areas.
Also, be sure to have newly acquired birds treated for worms before you introduce them to your existing birds.