It kind of looks like downy mildew.

It does look like powdery mildew. How are you watering? Is water getting splashed up onto the stems?

Here is a link that might be useful: What's Growing On?

I water at the base, but it's possible some splashes onto the stems. It's so hot and dry here that I never thought I would get mildew. What would you suggest that isn't too pricy to treat it with?

Hope someone answers this. I have the same thing! It's 102 minimum these days, I have to water. I don't understand why hitting the stems is such a big deal. It doesn't rain from the bottom after all.

SOME fungal and bacterial disorders are spread by water droplets, alys...whether rain or irrigation. Powdery mildew is not one of them.

I'm not seeing anything in this photograph that screams powdery OR downy mildew to me. Do the leaves look ok...top and underneath?

SOME fungal disorders are spread by water droplets, alys...whether rain or irrigation. Powdery mildew is not one of them.

I'm not seeing anything in this photograph that screams powdery OR downy mildew to me. Do the leaves look ok...top and underneath? How about some more pictures?

I ended up pulling it about a week ago, it just kept dying and the white fuzzy spots were covering everything, even though I tried a few of the remedies I found online. I'll just have to keep an eye on them if I plant more next year.

Thanks everyone!

I have two of my Zucchini trees has the same problem. I think it is fungal infection. I sprayed with copper I see the damage is stabilizing but the trees were devastated any way. I a going to use another chemical fungal spray with the hope to stop the spread to the rest of the trees.

This is my first year garden too, and my summer squash had the same spots, but they were on the leaves. I couldn't see down to the bottom because realized too late that I'd planted too thickly. Initially, I tried cutting off each leaf that had the powdery white spots. That slowed down the speed of the spreading, but it would still spread. I was careful to wash all my garden tools as well to prevent spreading the fungus, and I also watered from a soaker hose, never on top. I thought because it had been so hot, fungus wouldn't be a problem, but it was! I was chopping off so many powdery mildew leaved, I was afraid it would inhibit production. So, off I went to the store to pick up some Daconil. So far, I've done three applications, and everything looks MUCH better. However, I still see lingering signs of powdery mildew trying to rear it's ugly head. Try treating with a fungicide. Powdery Mildew spreads SO, so quickly. Good luck to you. And, if it's not powdery mildew, then I don't know what it is.

Mine doesn't look exactly like the photo the OP posted. I'll try to get a photo this afternoon and post it. Mine is actually down low on the stem and quite thick, kind of looks like it has snow on it, swept into the branches? The picture will be better than my explanation.

Okay, so here is a not-so-great photo of my white spots. As you can see, not the same as the OP's spots. As I'm already the only person in the US who never has luck with zucchini, I don't want it to die. My plants look incredibly healthy; like some huge tropical plant from the Pleistocene Era. LOL But my babies always rot from the flower end. Lack of pollination? And now fuzzy white stuff growing on one. You can't see me, but I'm shaking my head in disgust.