I have nylon sheers on all the windows of my apartment and they have
turned from white to a dingy gray color.  I have tried washing them in
detergent and an "Oxy-clean" type of soak and they are still gray.  Is
there any way to get them brighter / whiter? I can't use bleach on
them.

Hi redneckmystic,

Now that?s an intersting name!  

Here is a list of some commercial products that appear like a good
solution for your graying curtains:

=============================
Commercial Cleaning Products:
=============================

Restoration Cleaner
-------------------
?Removes Yellowing: mystery spots & yellowing caused by water damage,
age, UV rays and even discolored fold lines
Will not harm fine delicate material fibers: Contains no chlorine,
will not leave residue or harm fibers in any way?
http://www.worldatmydoor.com/sitePage.asp?site_id=51402&Page_number=3

Read some testimonials and see a picture of a restored baby bonnet:
http://www.worldatmydoor.com/sitePage.asp?site_id=51402&Page_number=12


Mrs. Stewart's Bluing
---------------------
?Mrs. Stewart's Bluing is a simple, concentrated blue liquid that
optically whitens white fabric. It does not remove stains, does not
"clean", but adds a microscopic blue particle to white fabric which
has been giving fabric that "just bought" whiteness for 115 years!?
http://j-walkblog.com/blog/index/P11050/

Mrs. Stewart?s web site:
http://www.mrsstewart.com/

Mrs. Stewart?s Bluing can be bought here
https://www.ugwhite.com/cgi-bin/store/agora.cgi?product=stewart&cart_id=

and here:
http://www.jensco.com/mrsstewliqbl.html


Rit Whitener And Brightener
----------------------------
?Or use Rit Whitener & Brightener to safely remove the stains and
brighten yellowed, dingy white fabrics without bleach. Note that White
Wash can only be used on white fabrics, while Whitener & Brightener
can be used on colored fabrics.?
http://peninsulaclarion.com/stories/121003/gif_121003gg008002.html

?If the fabric is white, consider specialty products available in
grocery or drug stores, such as Rit's "Whitener and Brightener" to
whiten the fabric.?
http://www.fabriclink.com/fabricstains/Dinginess.html
You can find the product easily in stores that sell Rit Dye products.
Some grocery stores sell Rit products, although craft and fabric shops
may be your best bet.
This online store sells Rit Whitener and Brightener
http://www.ritdye.com/store/liquid_whitener.asp



PDC Cleaning Product
---------------------
This product appears to clean *anything*!
?Restore old dingy linens, yellowed window sheers, antique rugs,
wedding dresses, etc. Soak in a solution of 2-4 ounces of PDC per
gallon of water for one hour (or longer if necessary) and rinse.?
http://www.decktechs.com/pdc_instructions.htm

=============================
Home Method:
=============================
?Bleaching synthetics - Use 2 cups vinegar in 6 cups water and rinse
in bluing solution.
http://stonecoldsober.deep-ice.com/frugalities/frugalcleaning.html


Hope this helps you brighten your sheers! Please ask for an Answer
Clarification, before rating, if any part of my answer is unclear.

Regards,
crabcakes

Nylon whitening products
Whitening synthetic fabrics

As always... Google does great work!