The motions of floating structure critically influence the work that floating offshore construction vessels can carry out. In the past, the roll motions of such structures have had the most dominant influence. As a result, different techniques have been proposed in order to reduce such roll motions. Nowadays, the investigations have moved one step forward and they have been focused not only on reducing roll, but also heave motions. In addition, the desire of controlling these motions for operational purposes has become essential. The use of air trapped in cavities has appeared as a good choice to fulfil all these requirements. For this reason, this thesis presents a time domain analysis of such a system, including its use in a practical application. The first part of this project consists of an overview of existing methods to reduce wave motions, together with the possibilities available to control them. It is followed by a critical comparison between methods in order to choose an optimal strategy to improve the response when working under particular conditions. After that, the equations of motions to represent the effect of pneumatic compliance are developed by making some assumptions. This is followed by the design and validation of a time domain solution, using Sesam to represent the effect of the waves on the structure, and Matlab, to solve the numerical problem. The results are tested against experimental data and the code is used for a case study. It consists of a pontoon, where the main objective is to check the influence of the air tanks allocation. Therefore, two different configurations are proposed and compared against each other. The analysis shows that the response can be greatly improved by increasing the size of the cavities, and that the optimal response can be achieved by controlling the pressure inside the tanks depending on the wave frequency. Keywords Air trapped cavities, pneumatic compliance, active control, time domain analysis, pontoon.