The article deals with the dating of Ugaritic letter RS 34.129 mentioning Shekelesh, one of the tribes belonging to the «Sea Peoples». Using the data of letters RS 18.038, RS 88.2158, RS 94 2530 and RS 2523, the author assumes that RS 34.129 was writ- ten by the Hittite king Tudhaliya IV not long before 1219 BC (according to Middle Egyptian chronology of the New Kingdom). The author believes as well that the data of RS 94.2530 and RS 94.2523 provide the information proving that the Ugaritic king Ammurapi’s reign lasted for 30 years at least. In the last part of the paper the author reconstructs Hittite-Ugaritic relations at the end of the 13th century BC. In his opin- ion, temporary decline of the Hittite kingdom during the short reign of Arnuwanda III was the cause of Ammurapi’s attempt to seek protection of Pharaoh Merneptah. But the events in Egypt after Merneptah’s death, connected with the struggle between Sethos II and Amnenmessu, made Ugarit come back under the rule of the next and last Hittite king Suppiluliuma II.