The subject of the first part of this paper is the evolution of liability for petty offences and administrative infringements under the Polish and Czechoslovak law. The basis phases of this evolution mark: the Polish regulation 1928 on penal-administrative proceeding, the Polish petty offences act 1932, the Czechoslovak four codification acts 1950, the Polish act 1951 on penal administrative jurisdiction, the Czechoslovak act on disciplinary offences 1957, the Czechoslovak reform of petty offences law 1961, the Polish act 1966 transforming some crimes into petty offences, the Czechoslovak act 1969 on offences, the Polish petty offences code with petty offences proceeding code 1971. Investigation of this evolution permits to observe changing tasks of criminal courts at the realization of liability for petty offences and appearing tasks of administrative courts at the realization of liability for administrative infringements. The next phases of this evolution after political transformation will be subject of the second part of this paper.