Invented in the mid-1980s, we are currently witnessing large-scale development of multitouch interfaces. Compared with the traditional mouse, multitouch displays require rethinking from scratch interaction techniques in order to understand the changes brought by this technology and formulate new theories. Manipulating three-dimensional (3-D) objects require the control of six degrees of freedom. Three are responsible for the object's position and three control the orientation. In this work, we focused on 3-D manipulation of an object using multitouch displays. Specifically, we studied the relationship between the input device (the multitouch display) and the task (3-D manipulation). First, we introduced a taxonomy for the representation of 3-D interaction techniques specific to multitouch displays. This taxonomy allowed us to highlight the influence of design strategies in terms of integration of degrees of freedom. Subsequently, we conducted a study of interaction techniques for 3-D positioning of an object. We presented two new techniques, which take advantage of capabilities offered by multitouch displays. The evaluation of these techniques revealed us results regarding the user coordination in realizing the task. Finally, we introduced a new interaction technique to handle 3-D manipulation. This technique was evaluated faster than existing techniques and we were able to determine the reasons for the improved performance. This work, which focus on the user coordination when using multitouch displays to perform 3-D tasks, recommend an approach that favors the separation of degrees of free- dom, in order to parallelize the user actions so as to take advantage of the extra input bandwidth offered by this type of input devices.