  Stellar kinematics provides the key to understanding star formation process.
In this respect, we present a kinematic study of the Monoceros OB1 (Mon OB1)
and R1 (Mon R1) associations using the recent Gaia data and radial velocities
of stars derived from high-resolution spectroscopy and the literature. A total
of 728 members are selected using the criteria based on the intrinsic
properties of young stars, parallaxes, and proper motions. The spatial
distribution and kinematic properties of members show that these associations
have distinct substructures. In Mon OB1, we find one northern group and two
southern groups. Mon R1 is composed of three small stellar groups that are
spatially and kinematically distinct. Some stars are found in a halo around
these two associations. We detect patterns of expansion for most stellar groups
in the associations. In addition, two stellar groups in Mon OB1 show the
signature of rotation, which provides an important constraint on cluster
formation. The star formation history of Mon OB1 is slightly revised. Star
formation first occurred in the southern region and subsequently in the
northern region. Recent star-forming events ignited deeper into the southern
region, while some stars are escaping from Mon OB1, forming a halo. Mon R1
might have formed at the same epoch as the formation of the northern group in
Mon OB1. Given that star formation is taking place on different scales along a
large arc-like structure, Mon OB1 and Mon R1 may be the results of hierarchical
star formation.
