Answer: These plants are interesting in that they can present an almost infinite variation of growth. The dry looking part may be the result of underwatering at some point -- the cactus name is a misnomer and they do require regular watering when in active growth and occasional watering while resting in fall and winter. Or, it might be caused by a pest infestation such as mealy bug or scale. Look at it carefully and if you see any white fuzzy spots (insect), wipe them off with a cotton swab dipped in rubbing alcohol. There is also the possibility of a canker or other infection in the dried portion of the stems. For this reason you may want to root some tip cuttings from healthy-looking portions of the plant as insurance. To do that, take a tip several sections long (or if that is not possible at least a half inch minimum), allow it to air dry for a day or so, then insert top end up into a soilless potting mix. Keep it barely damp and set it in indirect light such as a north window. It should root in a month or two. You could also consider removing the dried portions entirely and allowing the healthy looking base portion to regrow.
You may find the following pages about these plants interesting... the author, Ron Smith at the University of Nebraska, truly enjoys these plants and it shows. Reading through the questions and answers may also help you troubleshoot more specifically.
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