Russia's constitutional court is examining whether the language law, which forces ethnic groups in Russia to use the Cyrillic script, is legal.
President Putin aims to strengthen the Russian state by centralisation
The case was brought by officials from the Russian republic of Tatarstan, who want to use the Latin alphabet to express the local language.
Tatarstan argues the federal law violates the Russian constitution.
If they lose, it will be seen as a victory for the Kremlin's attempts to assert control over Russia's regions.
When President Vladimir Putin came to power more than four years ago, one of his priorities was to erode the power of the regions and boost Moscow's control over the whole of Russia - the aim being to strengthen the state through centralisation.
The Kremlin set about its task in the field of politics, in the economy and also in the area of language.
Challenge to authority
In 2002, the federal law on language was amended to decree that in Russia, a country with more than a 150 ethnic groups, only the Cyrillic alphabet could be used for local tongues.
That came as a blow to Tatarstan, a Russian region which had enjoyed considerable autonomy under Boris Yeltsin and which had already decided to switch its local language, Tatar, from Cyrillic to the Latin script.
The local authority argued that the Tatar language was better suited to Latin letters.
But the move was interpreted by Moscow as a challenge to its authority.
Now Russia's constitutional court will decide.
It is hearing arguments from Tatar officials as well as from a local lawyer from the region's capital, Kazan, who is defending the Cyrillic alphabet.