Alasgarov was also an Honorary Doctor of the Kiev State University.

On October 16, 1996, he was elected the Speaker of the National Assembly by the members of the parliament and re-elected on November 24, 2000.

In the 2005 parliamentary elections, Alasgarov was re-elected to the parliament from Garadag district of Baku.

[1] According to media reports, Alasgarov's health was deteriorating due to diabetes, which is why he did not run for re-election in November 2010.

Alasgarov was a member of Azerbaijani Lawyers and International Law Associations.