In the last years, there is an increasing interest in the manner that transversal competences (TC) are introduced in the curricula. Transversal competences aregeneric and relevant skills that students have to developthroughthe several stages of the educational degrees. This paper explain the context of TC in Higher Studies at the Universitat Politecnica de Valencia (UPV), Spain, where several working groups have been established in the last two years in order to improve the way both Technical Schools and lecturers/professors teach and assessthe degree of development of transversal competences (TC) in students. The UPV has promoted to grant variousinnovative educational projects that contribute to improve the assessment and collection of evidences on TC. This paper emerges from the work developed in one of these innovative educational projects and presents the experience related to the assessment of the TC "effective communication", specifically the written dimension of effective communication. The main aim of this paper is to analyse the assessment of effective communication in the context of postgraduate programmes at the UPV and, according to them, to develop and apply an assessment instrument. The developed assessment instrument comprises the relevant indicators to assessthe students written communication competency. It has been applied to evaluatethe assignments of students inthe course named" Production planning and scheduling in distributed environments", which belongs to the Master Degree in Advanced Engineering Production, Logistics and Supply Chain at the UPV. This paper presents both the educational experience and main results obtained.