Arbroath's Scottish Challenge Cup tie with Airdrieonians, Ayr United's quarter-final visit to St Johnstone and Stranraer v Clyde in League 2 have been postponed.
The game at Gayfield is off because of high winds, while there are waterlogged pitches at Saints' McDiarmid Park and Stranraer's Stair Park.
In the games that did go ahead, Inverness Caledonian Thistle and Raith Rovers have reached the Challenge Cup semi-finals.
Rovers beat Championship rivals Queen's Park after a penalty shoot-out following a 1-1 draw in Glasgow, while Caley Thistle edged out visitors Stenhousemuir 1-0 in a match between the top two in League 1.
Meanwhile, Spartans opened up an eight-point gap at the top of League 2 with a 6-0 thrashing of second-top hosts East Kilbride.
Two of Saturday's SPFL fixtures – Dundee United v St Mirren in the top flight and Montrose v Peterhead in League 1 – were postponed.
Motherwell v Aberdeen in the Premiership has been pushed back a day to Sunday, 15 February, with a 14:30 kick-off, at the request of the clubs.
Tuesday's Scottish postponements
Challenge Cup
Arbroath P-P Airdrieonians
St Johnstone P-P Ayr United
League 2
Stranraer P-P Clyde
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