The kinematic-dynamo problem with steady Beltrami flows at high magnetic Reynolds number is studied by a local analysis along unstable Lagrangian trajectories in the chaotic region and from some global considerations. The chaos properties of the flow, especially the local characteristic directions, are related to the time evolution and to the spatial distribution of the field solutions derived from the local analysis. Global considerations show that there are some integral constraints that a growing eigenmode of the magnetic field should satisfy, and an antidynamo result is given for the understanding of why some chaotic flows are not capable of fast dynamo action. ©1998 American Institute of Physics.