Glasgow Airport reported its busiest October for eight years after 836,798 passengers travelled through its doors - an annual increase of 14%.
Edinburgh recorded a sixth consecutive month with more than one million passengers.
That represented a 9.7% increase in passenger traffic from the same month last year.
At Glasgow, international traffic grew by 18.5% as a result of strong demand for European services, with Icelandair and Wizz Air both reporting a particularly busy month.
Airport bosses also reported a "significant uplift" on long haul services to Toronto, Florida and Dubai.
Domestic traffic increased by 8.9%, which the airport said was due to a strong demand from both business and leisure travellers on London services and regional routes.
In October, Glasgow - which is owned by AGS Airports - was crowned UK Airport of the Year at the National Transport Awards in London.
Managing director Amanda McMillan said: "It's been another fantastic month for the airport in terms of passenger growth and route development, but being crowned UK Airport of the Year was the real highlight.
"We have now enjoyed 11 consecutive months of double-digit growth and have added an additional one million passengers since October 2014 which is a huge milestone."
Edinburgh attributed its success in part to the continued strong performance of routes across the UK, as well as European destinations.
Chief executive Gordon Dewar described its run of a million passengers a month as a "tremendous achievement".
He added: "This record-breaking performance is a sure sign of the growing success of both Scotland and Edinburgh as a destination and also emphasises our position as a key driver for Scotland's economic growth."
Passenger numbers have continued to take off at Scotland's two busiest airports.