Oral and written skills are increasingly considered to be essential tools in the job market for the success of any worker, and are thus called soft skills. Nevertheless, most graduates who enter the labor market experience difficulties in the apprehension of communication, not only with regard to writing, but also in oral communication. These difficulties are also noticeable in the classroom, for instance when students need to participate by expressing their doubts when they have to present research work within the curricular units they attend, or when they have to write their answers in assessment tests. In this paper, we explore the communication skills of students from different graduate degrees (n = 345) in order to understand how they prepare for oral and written communication. We made use of the Personal Report of Communication Apprehension (PRCA), validated by McCroskey, Beatty, Kearney, and Plax (1985), in order to understand students' oral communication apprehension. To understand the levels of written communication apprehension, we applied the Daly--Miller Writing Apprehension Test (DMWA). We thus analyzed the communicational skills and the communication apprehension of students from social and human sciences courses in order to understand how they prepare for oral and writing communication, and whether there were differences between genders and between different graduate courses regarding communication apprehension. The main results of this research confirm that the students experienced difficulties with and fear of communication, especially for oral communication. Furthermore, the results indicate that female students showed more significant levels of anxiety with regard to oral and written communication than male students. This exploratory study also makes it possible to distinguish areas of communication apprehension according to the different genders, and even with regard to the degree courses students belonged to.