IEnumerable and order

I have got a question about the order in IEnumerable.

As far as I am aware, iterating through IEnumerable is pseudo-code can be written in the following way:

while (enumerable.HasNext())
{
    object obj = enumerable.Current;
    ...
}

Now, assume, that one needs to operate on a sorted collection. Can IEnumerable be used in this case or is it better to try other means (i.e. IList) with indexation support?

In other words: does the contract of IEnumerable make any guarantees about the order in general?

So, IEnumerable is not a proper mean for a generic interface that guarantees ordering. The new question is what interface or class should be used for an immutable collection with order? ReadonlyCollection? IList? Both of them contain Add() method (even is not implemented in the former one).

My own thoughts: IEnumerable does not provide any guarantees about the ordering. The correct implementation could return same elements in different order in different enumerations (consider an SQL query)

I am aware of LINQ First(), but if IEnumerable does not say a word about it's ordering, this extension is pretty useless.