Grassmann's law, named after its discoverer Hermann Grassmann, is a dissimilatory phonological process in Ancient Greek and Sanskrit which states that if an aspirated consonant is followed by another aspirated consonant in the next syllable, the first one loses the aspiration. The descriptive version was given for Sanskrit by Pāṇini.

Here are some examples in Greek of the effects of Grassmann's law:

In reduplication, which forms the perfect tense in both Greek and Sanskrit, if the initial consonant is aspirated, the prepended consonant is unaspirated by Grassmann's law. For instance /pʰy-ɔː/ φύω 'I grow' : /pe-pʰyː-ka/ πέφυκα 'I have grown'.

The fact that deaspiration in Greek took place after the change of Proto-Indo-European *bʰ, *dʰ, *gʰ to /pʰ, tʰ, kʰ/ (PIE *bʰn̥ǵʰús > παχύς (pakhús) not bakhús but Sanskrit बहु (bahú)) and the fact that all other Indo-European languages do not apply Grassmann's law both suggest that it was developed separately in Greek and Sanskrit (although quite possibly by areal influence spread across a then-contiguous Graeco-Aryan–speaking area) and so it was not inherited from Proto-Indo-European.

Also, Grassmann's law in Greek also affects the aspirate /h-/ < *s- developed specifically in Greek but not in Sanskrit or most other Indo-European. (For example, *ségʰō > *hekʰō > ἔχω /ékʰɔː/ "I have", with dissimilation of *h...kʰ, but the future tense *ségʰ-sō > ἕξω /hék-sɔː/ "I will have" was unaffected, as aspiration was lost before /s/.) The evidence from other languages is not strictly negative: many branches, including Sanskrit's closest relative, Iranian, merge the Proto-Indo-European voiced aspirated and unaspirated stops and so it is not possible to tell if Grassmann's law ever operated in them.

According to Filip De Decker, Grassmann's law had not operated in Mycenaean Greek yet, and it is almost certain that it occurred later than 1200 BC; it might even postdate the Homeric Greek period.

In Koine Greek, in cases other than reduplication, alternations involving labials and velars have been completely levelled, and Grassmann's law remains in effect only for the alternation between /t/ and /tʰ/, as in the last two examples above. (It makes no difference whether the /tʰ/ in question continues Proto-Indo-European *dʰ or *ɡʷʰ.)

Thus, alongside the pair ταχύς /takʰýs/ 'fast' : θάσσων /tʰássɔːn/ 'faster', displaying Grassmann's law, Greek has the pair παχύς /pakʰýs/ 'thick' : πάσσων /pássɔːn/ 'thicker' from the Proto-Indo-European etymon *bʰn̻ɡʰ- (established by cognate forms like Sanskrit बहु /bahú-/ 'abundant' since *bʰ is the only point of intersection between Greek /p/ and Sanskrit /b/) in which the /p/ in the comparative is a result of levelling. Similarly, πεύθομαι /peútʰomai/ ~ πυνθάνομαι /pyntʰánomai/ 'come to know' from PIE *bʰeudʰ- has the future πεύσομαι /peúsomai/. However, only /tʰ/ dissimilates before aspirated affixes like the aorist passive in /-tʰɛː/ and the imperative in /-tʰi/; /pʰ/ and /kʰ/ do not, as in φάθι /pʰátʰi/ 'speak!'.