Osthoff's law is an Indo-European sound law which states that long vowels shorten when followed by a resonant (Proto-Indo-European language (PIE) *m, *n, *l, *r, *y, *w), followed in turn by another consonant (i.e. in a closed syllable environment). It is named after German Indo-Europeanist Hermann Osthoff, who first formulated it.
The law operated in most of the Proto-Indo-European daughter languages, with notable exceptions being the Indo-Iranian and Tocharian branches in which the difference between long and short PIE diphthongs was clearly preserved.
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The term Osthoff's law is usually properly applied to the described phenomenon in Ancient Greek, which itself was an independent innovation from similar developments occurring in Latin and other Indo-European languages. However, often it is used in a loose sense, as a cover term referring to all shortening of long diphthongs in closed syllables.
Osthoff's law was in some versions valid for Greek, Latin, Celtic and Balto-Slavic, but not for Indo-Iranian and Tocharian. It also probably applied in Germanic, although there is very little evidence to support or refute that claim.