Remove zest or peel from oranges and set aside. Next, remove any seeds and white pith from the oranges. In a food processor, combine orange peel and orange sections until they are small pieces but not pureed.
Heat the oranges, pineapple, lemon or lime juice and sugar in a large, heavy-bottomed saucepan. Bring to the boil, then simmer to the desired thickness - usually between 30 minutes and a hour, stirring all the time.
Carefully pour into jars or freezer containers; let them cool for a few hours. Cover and refrigerate for up to 3 weeks or freeze for up to 1 year.