They do stretch a little over time. I have kite flying lines from Dyneema and Spectra, and they stretch over time and need to be equalized (move the knots so the lengths match).
But it's very little, I had about 2.5cm change in 25m over a few years. That's 1 part in 1000. This is from irregular kite flying, so not under (very) high tension or constant stress.
I've seen spectra rope used to tow launch hang gliders. It resulted in a performance advantage over whatever it replaced because it could be much thinner and lighter.
Ultra-high-molecular-weight polyethylene (UHMWPE): https://en.wikipedia.org/wiki/Ultra-high-molecular-weight_po...
Dyneema vs. Kevlar data: http://bladebuster.ca/our-products/cut-resistant-clothing/dy...
Dyneema vs. Kevlar and new fibers for military: www.army-technology.com/features/feature98985/
Zylon that was used instead of Kevlar degraded due to body moisture: https://www.npr.org/templates/story/story.php?storyId=473209...
Spectra a polyethylene fiber from Honeywell:: https://www.honeywell-spectra.com/applications/textiles/
UHMWPE used in ropes: www.novabraid.com/rope-material/spectra-fiber-rope/