They are a law to themselves, even though they do not have the law. The second half of this verse merely repeats what has gone before. However the phrase, a law to themselves needs to be looked at. It can be taken in two ways. If the gentiles are non-christians, then by doing what the law requires they are attesting to knowledge of the divine moral standards. Murray writes that by reason of what is implanted in their nature, they are confronted with the law of God. He says three things are true:
- The law of God confronts non-christians and registers itself in their consciences by reason of what they natively and constitutionally are
- They do things which this law prescribes
- This doing is not by extraneous constraint but by natural impulse 
Moo and others basically agree that this is talking of gentiles attesting knowledge of divine moral standards.
However, if the gentiles are indeed Christians, a different view is necessary. Cranfield writes:
Although they [the gentile Christians] have not been brought up by virtue of their birth in possession of God’s law, they now know it and actually have in their hearts the earnest desire to obey. 
V15 They Show that what the law requires is written on their hearts. The main question here is does this refer to a parallel with Jeremiah 31:33? Objections to the parallel are two fold:
- Jeremiah talks of the laws being written on their hearts and a complete knowledge of God that results from it. This result is an eschatological work of God wrought upon Israel. The present passage (Rom 2:14-15), however, is concerned with a non-eschatological fact of gentile life.
- V15 in most translations miss out the word ‘work’, hence the work of the law written upon their hearts. Murray says that there is a big difference from the requirement of the law written upon hearts than the law itself. If this refers merely to the requirement of the law, then it would be acceptable to equate this phrase with the equivalence of the things of the law. So there are innate moral laws written upon the hearts of every unregenerate person. Moo also comments that while in Jeremiah the final judgment of the people is not in doubt, here it is.
Cranfield, however, sees this as a deliberate reminiscence of Jeremiah. Cranfield has no problem with the eschatological element. Paul clearly believed that God’s eschatological promises were already beginning to be fulfilled through the gospel in believers lives. In this he is in agreement with the Already…not yet paradox which Moo so heavily emphasizes in his commentary. Therefore, for Cranfield, the eschatological objection is removed. He writes:
Here ‘the work which the law requires’ means not the required work as accomplished but the required work in the sense of the commandments contained in the law. 
Also, Cranfield points out that the LXX version of Jeremiah 31:33 is so close to v15 that it is difficult to avoid the conclusion that Paul has Jeremiah in mind. 2 Cor 3:2-3 says You yourselves are our letter, written on our hearts, known and read by everyone, revealing that you are a letter of Christ, delivered by us, written not with ink but by the Spirit of the living God, not on stone tablets but on tablets of human hearts.
This passage was addressed to gentile Christians. The objection that the phrase written on their hearts is a very common one is negligible. It is not common in Paul and surely Paul would have known the significance of using such a phrase.
 John Murray NICNT To The Romans pg 73
 Cranfield pg157
 Cranfield pg158