Could you, please tell if the sentence below sound OK in English?
"In those countries DOT programs are not only state responsibility but non-governmental, religious and charity organizations also give their contribution."
In those countries, the state does not assume sole responsibility for DOT programs; non-governmental organizations, such as charities, and faith-based initiatives also play a role.
1. Charities, such as Oxfam, are NGOs
2. Depending on your audience, you might get away with writing 'NGOs' instead of 'non-governmental organizations' - the term has become widely used and understood (I would say quite recently) and the abbreviation is often used in the media (eg on the BBC or in the Guardian newspaper) for brevity and without explanation.
3. I've written 'faith-based initiatives' partly as a way of getting round my uncertainty as to whether you are referring to religious bodies such as the Catholic Church or organizations set up by religious bodies for charitable puposes. Also, if the latter these come under charities so you'd have to write 'including faith-based and other charities', which isn't very good, or rephrase the sentence.