The thienylazolylalkoxyethanamines (I) where R1 is a hydrogen atom, a halogen atom or a lower alkyl radical; R2, R3 and R4 represent, independently, a hydrogen atom or a lower alkyl radical; and Az represents a five-member nitrogenated hetercyclic aromatic group, N-methyl-substituted, that contains from one to three nitrogen atoms. They have analgesic activity in mammals, including humans. The compounds (I) can be obtained, for example, by reaction of a derivative of hydroxy-thienylazol (IV) with a derivative of a suitable N-(ethyl)amine. The compounds (IV) are useful intermediates in the synthesis of the compounds (I). The compounds (I) have an application in human and/or veterinary medicine.