The main topic of this article comprises four unpublished Arabic texts on astrolabe-like instruments for showing the conditions of eclipses. They are the earliest technical descriptions of eclipse computers in any language. The first text is a treatise by ʿAlī ibn ʿĪsā (ninth century) on a special astrolabe for lunar phases and eclipses. The second text is an anonymous redaction of the first text with some omissions and additions. The third text describes a similar instrument with a different design, which was invented by Muḥammad ibn Muḥammad Nasṭūlus al-Asṭurlābī in the year 893/894 ce. The fourth anonymous text describes a plate for a graphical solution of the size of a lunar eclipse. In the concluding part, later Arabic descriptions of eclipse computers are summarized, some traces of these texts on real astrolabes are mentioned, and finally some comparable medieval Latin texts are referred to. Four Appendices contain an edition of the Arabic texts and English translations.