There is already known a therapeutic composition useful in particular as coronary vasodilatator and as antispasmodic drug, comprising, as active ingredient, a phenoxyalkylamine having the formula: ##SPC3## In which n is zero or 1, R is hydrogen or a hydroxy group, R1 is an alkyl group and R2 is hydrogen, a hydroxy group or an alkyl group, R2 being other than hydroxy when n is equal to zero, or a p