Laser cutting of CFRP lightweight parts has the advantages of a contact-free, automatable and flexible processing for a prospective series production. For the development of strategies for laser cutting of carbon fibre reinforced plastics (CFRP), different scientific approaches exist to achieve a process with small heat affected zones (HAZ), and high cutting rates. Within this paper a cw laser, a nanosecond and a picosecond laser source emitting in the near infrared range have been used in combination with a scanning system to cut CFRP with a thermoplastic matrix. The influence of the scanning speed on the size of the HAZ and the corresponding tensile strength were investigated for each laser source. Furthermore, the authors compared the achievable HAZ and the effective cutting speeds of the different setups in order to evaluate the efficiency and quality of the chosen strategies. The results show that a nanosecond pulsed laser source with high average power is a good trade-off between attainable quality and cutting rate.