Physical Layer Network coding (PLNC) can significantly improve network performance, but some security issues arise due to the limited information available to the forwarders. This paper analyses authentication in networks with PLNC and show theoretical and practical security limits. In particular, we obtain a lower bound for the probability of an attacker being able to insert a false message such that the message is believed to come from a legitimate source. We prove that an information-theoretic bound similar to the one for point-to-point communication systems can be achieved in networks employing PLNC. Necessary and sufficient conditions to achieve the bound are identified. Finally, a simple but important modification of a previous scheme is proposed to achieve the obtained bound.