We present a new study of kinematical problems of relativistic nucleon-nucleon interactions, more complete than the previous studies. Two-component spinor formalism is used throughout. Several choices of spinor bases, their relations, crossing relations in all channels, helicity amplitudes, partial-wave amplitudes, the absence of kinematical singularities, and unitarity are discussed. The contributions of arbitrary intermediate states J in the unitarity are summed and the Regge forms for all five scalar amplitudes are obtained.