Processes comprising: (a) providing a feed stream comprising a C4 compound having at least a nonaromatic C—C double bond or C—C triple bond; (b) contacting the feed stream with an adsorbent which has been activated at a temperature of 450 to 1000° C. comprising at least 3% by weight of aluminum oxide to remove one or more impurities from the feed stream; and (c) contacting the feed stream from which one or more impurities have been removed with a metathesis catalyst under metathesis reaction conditions to form a compound or a mixture of compounds having a nonaromatic C—C double bond or C—C triple bond.