The present invention relates to amorphous transparent copolyamides of formula: PACM.T/D.X/X1.Y1 resulting from the condensation of PACM, terephtalic acid, a diamine D, a diacid X, a diamine X1 and a diacid Y1 in which: PACM denotes the p-bis(aminocyclohexyl)methane, T denotes terephtalic acid, D denotes a diamine chosen from aromatic, arylaliphatic and cycloaliphatic diamines, X denotes a diacid HOOC—(CH2)n—COOH having from 8 to 20 carbon atoms, X1 denotes an aliphatic diamine, Y1 denotes a diacid HOOC—(CH2)n—COOH having from 6 to 20 carbon atoms, the mol proportion of PACM.T is such as (PACM.T)/(PACM.T+D.X) is above 0.5, and can be increased to 1, the mol proportion of X1 is between 16% and 38%, X1.Y1 can be replaced partly or totally by Z, a lactam or an alpha-omega aminocarboxylic acid, having from 9 to 20 carbon atoms, and in this case the mol proportion of Z is between 33% and 75%.