In a process for selectively separating 1-butene from a C4 feed stream comprising at least 1-butene, cis-2-butene and trans-2-butene, the feed stream is passed through a first bed of an adsorbent comprising a crystalline microporous material to form a substantially trans-2-butene-free effluent stream. Then, the substantially trans-2-butene-free effluent stream is passed through a second bed of an adsorbent comprising a crystalline microporous material to form a substantially 1-butene-free effluent stream, whereby the 1-butene is separated from the feed stream. The adsorbed 1-butene is then typically desorbed from the second adsorbent bed either by lowering the pressure or raising the temperature of the bed.