The structural and growth polarities of centrosomal and chromosomal microtubules were studied by analyzing the kinetics of growth of these microtubules and those initiated by flagellar seeds. By comparing rates of elongation of centrosomal and flagellar-seeded microtubules, we determined whether the centrosomal microtubules were free to grow at their plus ends only, minus ends only, or at both ends. Our results show that centrosomal microtubules elongate at a rate corresponding to the addition of subunits at the plus end only. The depolymerization rate was also equivalent to that for the plus end only. Chromosomal microtubule elongation was similar to the centrosome-initiated growth. Since the data do not support the hypothesis that both ends of these spindle microtubules are able to interact with monomer in solution, then growth must occur only distal or only proximal to the organizing centers, implying that the opposite end is unavailable for exchange of subunits. Experiments with flagellar-seeded microtubules serving as internal controls indicated that the inactivity of the minus end could not be accounted for by a diffusible inhibitor, suggesting a structural explanation. Since there is no apparent way in which the distal ends may be capped, whereas the proximal ends are embedded in the pericentriolar cloud, we conclude that centrosomal microtubules are oriented with their plus ends distal to the site of nucleation. A similar analysis for chromosomal microtubules suggests that they too must be oriented with their plus ends distal to the site of initiation.