The mooring systems give stability to the floating platforms against environmental conditions, stabilizing the platform with mooring lines attached to the seabed. The mooring systems are among the main components that guarantee the safety of the staff and the various operations carried out on the platforms. The current approaches used to monitor mooring lines are inefficient as line tension sensors are expensive to install, maintain, and have durability problems. This article presents the development of two neural network-based machine learning systems: a Multilayer Perceptron (MLP) and a Long Short-Term Memory (LSTM). They are able to detect mooring line failure in near real-time based on the comparison between measured and predicted motion. The implemented systems were trained and evaluated with simulated motion data generated using real environmental conditions measured in the Campos Basin, in Rio de Janeiro, Brazil. The results showed the MLP and LSTM models were able to detect a failure in the mooring lines, with increasing difference between the predicted and the measured motions when there is a line breakage. A comparison between the two machine learning models revealed the LSTM model performed better at predicting the motions of the platform.