A compound having the formula I: R1-Z-R2 (I) or a pharmaceutically acceptable salt or solvate thereof； wherein R1 is hydrogen, C1-4 alkyl, acetyl, formyl, benzoyl or trifluoroacetyl； R2 is OH or NH2； and Z is an amino acid sequence that comes from the sequence of formula Ia: ** Formula ** and also comprises at least four amino acid substitutions or deletions that are only at positions in the sequence selected from 2, 3, 4, 9 , 10, 15, 16, 17, 20, 21, 24, 28 and 29, as follows: X2 is selected from Aib and Ala； X3 is selected from His, Pro, Dab (Ac), Dap (Ac) and Gln (Me)； X4 is DAla； X9 is Glu； X10 is selected from Val, Leu, N-Me-Tyr and N-Me-DTyr； X15 is Glu； X16 is selected from Aib, Lys, Glu, Leu, Val, DVal, Phe, His, Arg, Pro, DPro, N-Me-Ser and N-Me-DSer； X17 is selected between Ala and Ser； X20 is selected from Glu and Lys； X21 is selected from Glu, Lys and Ser； X24 is selected from Lys, Ser, Glu and Ala； X28 is selected from Ser and Lys, and Glu, or is absent； X29 is selected between Ser and Ala, or is absent； with the proviso that Z is not selected from: HSQGTFTSDYSKYLDSARAEDFVKWLEST； and HSQGTFTSDYSKYLESRRAKEFVEWLEST； wherein the compound has glucagon agonist activity and improved solubility and / or stability compared to native human glucagon.Un compuesto que tiene la formula I: R1-Z-R2 (I) o una sal o un solvato farmaceuticamente aceptables del mismo； en el que R1 es hidrogeno, alquilo C1-4, acetilo, formilo, benzoilo o trifluoroacetilo； R2 es OH o NH2； y Z es una secuencia de aminoacidos que procede de la secuencia de formula Ia:**Fórmula** y que comprende ademas al menos cuatro sustituciones o deleciones de aminoacidos que estan solamente en posiciones de la secuencia seleccionadas entre 2, 3, 4, 9, 10, 15, 16, 17, 20, 21, 24, 28 y 29, como sigue: X2 se selecciona entre Aib y Ala； X3 se selecciona entre His, Pro, Dab(Ac), Dap(Ac) y Gln(Me)； X4 es DAla； X9 es Glu； X10 se selecciona entre Val, Leu, N-Me-Tyr y N-Me-DTyr； X15 es Glu； X16 se selecciona entre
