A solid anhydrous composition for caring for and/or making up keratin materials comprising: a) at least one triglyceride oil according to formula (I): CH2(OOCR1)CH(OOCR2)CH2(OOCR3) (I) wherein R1, R2 and R3 are independently chosen from C6-C30 alkyl and C6-C30alkenyl; b) at least one triglyceride oil according to formula (II): CH2(OOCR1)CH(OOCR2)CH2(OOCR3) (II) wherein R1, R2 and R3 are independently chosen from C6-C30 alkyl and C6-C30alkenyl, at least one of R1, R2 and R3 is substituted with a hydroxyl; c) at least one pasty compound chosen from an ester of dimer dilinoleic acid and polyol(s) or an ester thereof, and d) at least one wax, wherein the triglyceride oil according to formula (I) and the triglyceride oil according to formula (II) are present in the solid anhydrous composition in a weight ratio less than or equal to 1:1.