Part I is a 12-month, open label treatment period in which doxycycline (200 mg/day, continuously) and tauroursodeoxycholic acid (750 mg/day continuously) are administered to 40 consenting subjects with transthyretin amyloidosis. Part II is a withdrawal period in which subjects will be monitored for disease progression. During part I, subjects will be evaluated at baseline (study Day 0), and then after 3, 6, 9 and 12 months of doxycycline plus tauroursodeoxycholic acid treatment or at premature treatment discontinuation; during part II, they will be assessed at months 15 and 18. Monthly phone contacts and blood tests will be performed to monitor potential adverse events.