  We present a covariant framework of kinematics in the dS spacetime, which is
a natural postulate of recent astronomical observations ($\Lambda>0)$.
One-particle states are presented explicitly. It is noticed that the dispersion
relation of free particles is dependent on the degrees of freedom of angular
momentum and spin. This fact can be referred to as the effects of the
cosmological constant on kinematics of particles. The kinematics in dS
spacetime is used to investigate the phenomenon of ultra high energy cosmic
rays. We emphasize the possibility of solving the threshold anomalies of the
interactions between ultra high energy cosmic rays and soft photons in the
covariant framework of kinematics in the dS spacetime.
