An amylin derivative comprising an amino acid sequence of Formula 1: ** (See sequence) ** where Xaa1 is removed or independently selected from Lys, Arg, His and Glu; Xaa3 is independently selected between Asn and Lys; Xaa14 is independently selected from Glu, Asn, Gln and Asp; Xaa17 is independently selected from His or Arg; Xaa18 is independently selected from His or Arg; Xaa21 is independently selected from Asp, Asn and Gln; Xaa24 is independently selected from Glu and Gly; Xaa25 is independently selected from Ala and Pro; Xaa26 is independently selected from Pro and Ile; Xaa28 is independently selected between Ser and Pro; Xaa29 is independently selected between Ser and Pro; Xaa31 is independently selected from Glu and Asn; end C can optionally be derivatized as an amide; wherein a substituent is connected to the amino acid residue Xaa1 or Cys in position 2, said substituent comprising an albumin binding moiety.Un derivado de amilina que comprende una secuencia de aminoácidos de Fórmula 1: **(Ver secuencia)** donde Xaa1 se elimina o se selecciona independientemente entre Lys, Arg, His y Glu; Xaa3 se selecciona independientemente entre Asn y Lys; Xaa14 se selecciona independientemente entre Glu, Asn, Gln y Asp; Xaa17 se selecciona independientemente entre His o Arg; Xaa18 se selecciona independientemente entre His o Arg; Xaa21 se selecciona independientemente entre Asp, Asn y Gln; Xaa24 se selecciona independientemente entre Glu y Gly; Xaa25 se selecciona independientemente entre Ala y Pro; Xaa26 se selecciona independientemente entre Pro e Ile; Xaa28 se selecciona independientemente entre Ser y Pro; Xaa29 se selecciona independientemente entre Ser y Pro; Xaa31 se selecciona independientemente entre Glu y Asn; el extremo C se puede derivatizar opcionalmente como una amida; donde un sustituyente se conecta al residuo aminoacídico Xaa1 o la Cys en la posición 2, comprendiendo dicho sustituyente un resto de unión a la albúmina.