The first two leaves were on a stem about 3' long. It was the only stem that had spots. The second two leaves were on the other plant and these spots appear to be different.

Are they inside or out? Mealies don't usually do this kind of damage - they're usually on new growth that often comes in distorted. Hmm...

Denise in Omaha

Looks like fungal spot from too wet conditions,excessive rain, moisture,or misting will cause it,especially if the plants are outside.Bacteria will penetrate any lesions or insect damage on the leaf surface and will rot the parts of the leaf.Any spray on fungicide will prevent the spread of it as well as less humid conditions for extended periods of time.I use Bonide Captan.

I suspected that this is fungal, but the spotted leaves were on only one stem on both plants, which I have cut out. The rest of both plants are healthy. I live on the Oregon Coast so humidity in the house is between 58% and 76% on a normal basis. I will be spraying them today with a fungicide that I have on hand, but will look for Bonide Captan as suggested by Jimmy. Thank you all for your input. It has shed some light on why my aloes are also showing brown spots.