This study includes up to a 3-week Screening Period, followed by a 52-week treatment period. Participants with CIC meeting the entry criteria received linaclotide 145 μg capsules, orally, once daily and participants with IBS-C meeting the entry criteria received linaclotide 290 μg capsules, orally, once daily. Participants with intolerable Adverse Events (AEs), following resolution of the AEs, could be randomized to receive 290 μg, 145 μg, or the lower dose of 72 μg linaclotide oral capsules for IBS-C; and 145 μg or 72 μg for CIC. Participants who experienced further intolerable AEs after the randomization could be transitioned to open-label 72 μg linaclotide.