One gear turns $ 33\frac{1}{3}=100/3 $ times in 60 seconds, so it turns 5/9 times in one second, or 5 times in 9 seconds. The other gear turns 45 times in 60 seconds, so it turns 3/4 times in one second, or 3 times in 4 seconds. To find out after how many seconds the two gears next have both their marks pointing due north, we have to find the least common multiple of $ 4=2^2 $ and $ 9=3^2 $, which is $ 2^2\cdot3^2=36 $. Therefore, the two gears next have both their marks pointing due north after $ \boxed{36} $ seconds. (One gear turns exactly $ 5\times4=20 $ times, and the other gear turns exactly $ 3\times9=27 $ times.)