New methodologies in the teaching and evaluation of two key generic competences Teamwork and Oral and Written Communication in the General Chemistry course in the Material Engineering degree of the University Rey Juan Carlos have been elaborated. To develop the competences we have used both chemistry laboratory and coursework assignments incorporating problem based learning exercises. The students working in groups have resolved the chemical problems posed and presented their results in a written report and an oral communication. Key to the success of our project has been the continuous evaluation in the development of the competences by the students using different indicators and descriptors in the assessment. This has allowed us to monitor the progress of the students in acquiring the competences in question. This paper forms part of our research into new models of competence based teaching and evaluation within the Educational Innovation Project "Competence Learning and Evaluation methods in University Education" directed by Dr. Sanjiv Prashar.