Context. Nearby late-type stars are excellent targets for seeking young objects in stellar associations and moving groups. The origin of these structures is still misunderstood, and lists of moving group members often change with time and also from author to author. Most members of these groups have been identified by means of kinematic criteria, leading to an important contamination of previous lists by old field stars. Aims. We attempt to identify unambiguous moving group members among a sample of nearby-late type stars by studying their kinematics, lithium abundance, chromospheric activity, and other age-related properties. Methods. High-resolution echelle spectra (R similar to 57 000) of a sample of nearby late-type stars are used to derive accurate radial velocities that are combined with the precise Hipparcos parallaxes and proper motions to compute galactic-spatial velocity components. Stars are classified as possible members of the classical moving groups according to their kinematics. The spectra are also used to study several age-related properties for young late-type stars, i.e., the equivalent width of the lithium Li I 6707.8 angstrom line or the R'(HK) index. Additional information like X-ray fluxes from the ROSAT All-Sky Survey or the presence of debris discs is also taken into account. The different age estimators are compared and the moving group membership of the kinematically selected candidates are discussed. Results. From a total list of 405 nearby stars, 102 have been classified as moving group candidates according to their kinematics. i.e., only similar to 25.2% of the sample. The number reduces when age estimates are considered, and only 26 moving group candidates (25.5% of the 102 candidates) have ages in agreement with the star having the same age as an MG member.