Kinematical Constraints on Helicity Amplitudes

The kinematical constraints satisfied by helicity amplitudes are derived by two methods. One uses extra kinematical symmetries, which are present whenever there are constraints. The other uses the connection between $M$ functions and helicity amplitudes. It is shown that the threshold and pseudothreshold constraints do not imply conspiracies between different Regge trajectories. The transitions between the different sets of $s=0\mathrm{}$ constraints (which change when masses become equal) are described.