Context. An OB association is a gravitationally unbound group of stars. The identification of the members of the association is an important aspect of its study. There are few astrometric membership studies for OB associations, but the combination of these studies with astrophysical techniques becomes a very powerful tool for this type of research. Aims. We perform new spectroscopic and astrometric studies of the members of the association Centaurus OB1 (Cen OB1) and the open cluster NGC 4755. Methods. To carry out this study we used new spectroscopic optical observations obtained at CASLEO, and proper motion and photometric data from the Tycho-2 Catalogue and other databases available via the Internet.Results. With this investigation we found 52 members of Cen OB1 (l = 303.• 7, b = 0.• 4) and four members of NGC 4755 (l = 303.• 2, b = 2.• 5), an open cluster integrated into the Cen OB1 stellar association. The distance, heliocentric radial velocity, proper motion, and age of Cen OB1 are 2.6 ± 0.5 kpc, ∼−20 km s −1 , μ α cos δ = −4.78 ± 0.10 mas yr −1 , μ δ = −0.93 ± 0.10 mas yr −1 , and ∼20 × 10 6 years old, respectively. The same parameters found for NGC 4755 are 1.9 ± 0.5 kpc, −18 ± 2 km s −1 , μ α cos δ = −4.14 ± 0.19 mas yr −1 , μ δ = −1.09 ± 0.12 mas yr −1 , and ∼15 × 10 6 years old. The pulsars PSR J1253−5820 and PSR J1254−6150 could have been born as the result of supernovae explosions that occurred in the past by massive members of Cen OB1. We have seen Infrared Astronomical Satellite (IRAS) sources near Cen OB1, that show that star formation is still occurring. The age gradient observed between the different members of Cen OB1 makes it likely that the stellar association and IRAS sources represent different stages of a sequential formation process.