Iterator of iterator
I don't see any reason to limit this to Integers.  The solution can be trivially genericized.

IteratorOfIterator is a clumsy name.  By analogy with Python's itertools.chain(), I suggest calling this class ChainIterator&lt;T&gt;.  You can rename the iteratorOfIterator private variable accordingly, too.

I suggest adding an alternate constructor that takes an Iterable&lt;Iterator&lt;T&gt;&gt;, for convenience.

The hasNext() method seems fine.  As for next(), the message in the NoSuchElementException that you throw seems a bit weird; I would just omit it.

With not much extra effort, you can add support for remove().

public class ChainIterator&lt;T&gt; implements Iterator&lt;T&gt; {

    private final Iterator&lt;Iterator&lt;T&gt;&gt; chain;
    private Iterator&lt;T&gt; currentIterator;
    private Iterator&lt;T&gt; lastIterator;

    public ChainIterator(Iterable&lt;Iterator&lt;T&gt;&gt; iterable)  {
        this(iterable.iterator());
    }

    public ChainIterator(Iterator&lt;Iterator&lt;T&gt;&gt; iterator)  {
        this.chain = iterator;
    }

    @Override
    public boolean hasNext() {
        while (currentIterator == null || !currentIterator.hasNext()) {
            if (!chain.hasNext()) return false;
            currentIterator = chain.next();
        }
        return true;
    }

    @Override
    public T next() {
        if (!this.hasNext()) {
            this.lastIterator = null;         // to disallow remove()
            throw new NoSuchElementException();
        }
        this.lastIterator = currentIterator;  // to support remove()
        return currentIterator.next();
    }

    @Override
    public void remove() {
        if (this.lastIterator == null) {
            throw new IllegalStateException();
        }
        this.lastIterator.remove();
    }
}