Two widely used signatures of interplanetary coronal mass ejections are counterstreaming suprathermal electrons, implying magnetic structures connected to the Sun at both ends, and magnetic clouds, characterized by large-scale field rotations, low temperature, and high field strength. In order to determine to what extent these signatures coincide, electron heat flux data were examined for 14 magnetic clouds detected by ISEE 3 and IMP 8 near solar maximum and 34 clouds detected by Wind near solar minimum. The percentage of time during each cloud passage that counterstreaming electrons were detected varied widely, from 6 clouds with essentially no counterstreaming to 8 clouds with nearly 100% counterstreaming. All of the former but less than half of the latter occurred near solar minimum, suggesting a possible solar cycle dependence on the degree of magnetic openness. The counterstreaming intervals were distributed randomly throughout the clouds, with a median length of 2.5 hours. A plot of counterstreaming percentages against cloud diameter for 33 clouds modeled as cylindrical flux ropes indicates a linear dependence of the percentage of closed flux on cloud size, with the largest clouds being the most closed. Overall the results are consistent with the view that although magnetic field lines within a magnetic cloud can form a large-scale, coherent structure, reconnection in remote regions of the structure, presumably near the Sun, sporadically alters its topology from closed to open until the cloud assimilates into the ambient solar wind. ¿ 2000 American Geophysical Union