While CaF2:Nd3+,Lu3+ spectroscopic features are now well-known for its broadband laser operation near 1 µm and its good quantum efficiency, this material is appealing for a number of applications such as mode-locking operation. In this paper, we investigate this crystal for dual-wavelength picosecond and femtosecond operations by using a semiconductor saturable absorber mirror (SESAM). In dual-wavelength picosecond operation, synchronous mode-locking is demonstrated at 1054 and 1059 nm when pumping at 797nm and when using a high reflective mirror as an output coupler. Only one pulse train at 93,8MHz was formed and the intensity autocorrelation trace shown a period beat frequency of 1.34 THz. Pumping at 791 nm led to the formation of two asynchronous mode-locked pulses probably because the two emission lines at 1049 nm and 1061 nm were too far to be coupled. Hence by spectral filtering it is possible to make a single train mode locked laser at 1061 nm generating femtosecond pulses. The laser generated modelocked pulses with pulse duration of 435 fs, average power of 10 mW, and central wavelength of 1061 nm. More output power could be obtained by using a more transmissivity for the output coupler however degrading other performances. These results open the way for further investigation on CaF2:Nd3+,Lu3+ crystals, with the aim of their implementation as active components in high power femtosecond lasers.