This study probes into the speech of simultaneous interpreters under the light of discourse analysis. In this context, some important and very visible elements are textual cohesion and coherence. The interpreter's discourse (Target Discourse - TD) is forged on the basis of the speaker's discourse (Source Discourse - SD), which is received by the interpreter as it is formulated. That means that it is based on an unfinished discourse, or a discourse that is still being processed, which is a heavy constraint. The author further analyses Interpreters´ strategies that broaden their comprehension of the SD and enable them to render a coherent and cohesive TD, in spite of the constraints.