Høgni Hoydal brought the Republican Party back up from four MPs to eight in the 1998 elections and into government, due to popular opinion at the time.

After these elections another coalition was formed leaving the Republican Party in opposition.

The negotiations, however, broke down and the Faroese coalition started going on a path towards greater autonomy by taking over the responsibility of matters previously undertaken by Denmark.

His son was the Faroese writer and politician Karsten Hoydal (1912–1990) who was born in Hoydalar.

Karsten Hoydal and his wife Marie Louise Falk-Rønne have four children: Annika Hoydal, born 1945, is an actor and singer, Gunnar Hoydal, born 1941 is also a writer, Kjartan Hoydal, born 1941 (Gunnar and Kjartan are twins) was secretary of the North East Atlantic Fisheries Commission (NEAFC) and is now director of sp/f Skrivarastova Fish and Film.