Read the care tag to check that your polyester-nylon drapes are machine washable and dryer safe. Some polyester-nylon drapes are labeled as "Dry clean only."
Completely unfold your machine washable drapery panels and place them in the dryer with a damp towel. Set the dryer to a low-heat setting suitable for synthetics. Synthetic fibers, including polyester and nylon, can melt and change texture when exposed to high heat. Tumble the drapery panels with the damp towel for about 30 minutes. Remove them from the dryer immediately and hang them, or lay them out somewhere flat until you can hang them.
Hang dry-clean-only panels or washable panels that are only lightly creased, and apply gentle steam with a hand-held steamer. Move from the top down and only lightly touch the fabric with the steaming wand. Steam the drapes from the reverse side if the panel is decorated on the front.
Spread out polyester-nylon drapery panels right side down on an ironing board and set your iron for its lowest synthetic setting -- if you don't have a steamer. Gently glide the iron over the fabric, avoiding pressing down. Nylon fabric is less tolerant of heat and pressure from the iron than polyester. If the fiber content of your drapery panels is more polyester than nylon, you may need to turn up the heat slightly and can press down a little harder if necessary.