The ramp rate limitation phenomena were studied using local field sensors to observe the intrinsic processes within the cable. Sensitive miniature Hall sensors and small pick-up coils placed around cable-in-conduit superconductor were used to measure local magnetic fields and field derivatives associated with currents in the cable. Using this method, both fast jumps and slow changes in local magnetic fields at different conditions mere observed. First jumps occured during ramping background magnetic field and may indicate a fast current redistribution processes. Slow changing of local fields may be associated with current loops closed through the current lead joints. Such current loops may also indicate the nonuniformity of current distribution in the cable strands. The new method is a promising tool for future investigations of stability of multistrand cables.