This article analyses the problem of international criminal liability for offences against cultural heritage. The author has considered three offences against cultural values: smuggling of cultural values, destruction of cultural goods and theft of cultural goods. The investigation of the offences against cultural values includes a number of aspects: the nature of the offences against cultural values; the advantages of the international or national character of the liability for the offences against cultural values; the circumstances of committing offences against cultural assets (for example the existence of an armed conflict); the objectives of committing offences against cultural values (their export as a treasure, the destruction of the cultural heritage; intimidation); the possible effects of the offences against cultural values. Based on these aspects, the author identifies a series of categories of offences against cultural assets. Each of these categories is analysed from the point of view of international liability.