I bought a few doll wigs for a new project I have been working on (will post completed puppets along with in-process pictures very soon! Considering that the puppets will be packed and unpacked and performed with quite a bit, I want them to retain their style as much as possible. I don't want to mess up the wigs though, they are modacrylic. What do you recommend? Thank you in advance!

Yep you can use hairspray on them if you want. Are the wigs sewn on?  The reason I ask this is because over time as you add more hairspray to hold the style, you'll start to see a build up on the wigs that may need to be washed out. Here are a few tips to make them last as long as you can without washing. Since they are puppets I bet you can go as long as a year before you would need to perhaps wash them out and start again.

Tip one: Do not use a lot of hair spray.  A very light once over should be enough.

Tip two: Hair spray that is already in the wig can be reactivated with water or alcohol.  Since in the pack the wigs are going to get pressed down and compacted, you are going to have to fluff them up when you unpack them. This really can't be avoided. Use a pick or large come to fluff the wig and the spritz with your water or alcohol. Water does not dry out the fibers of the wig and alcohol can. It all depends on the type of wig weather this is really going to be a problem. With what you are doing I doubt it will.

Tip three: Think about using thin fishing line or clear thread to help control your hair style. You can often hold back bangs and such in this way. It is hard to explain really since it really depends on what you are styling but keep this in the back of your mind as you look at your styles.  Barret's and hair decorations are also good for this. Remember though that even with this from time to time you have to re-do this be because the hairs can come out and get messy.

Last tip: Gluing hair in place really does not work. I tried once with some wigs to use a thin "glue" to keep the hair style rigid and in place.  Worked for about three performances and then the hairs still began to pull loose from the style and become fuzzy. Because I had the glue in the hair I was unable to clean up or neaten the hair style back into place with a comb or pick. Actually ended up having to clean out the glue with solvents and go back to plain old hair spray. 

Thanks for the tips Shawn! The wigs, for now, are pinned in place and I was planning to stitch them on. Does the hairspray affect the skin fabric of the puppet at all? And I'm glad you mentioned about the glue. A puppeteer suggested trying spray adhesive and I considered it for a brief second before shrugging it off since it would leave the hair sticky too.

Hairspray will leave a "coating" or build up on the fabric.  I would use a cleaner bag or plastic wrap to cover the fabric before I sprayed the hair.
A stiff hair spray ("Aussie freeze" is a good one)will keep the hair in place for a long time.  As with all hair sprays it will build up, but it can be washed out.

Pack your puppets so the hair has some space around it (think individual containers).  My personal preference is to pin the wigs on and take them off when the puppet is not being used.  We store ours on styrofoam wig heads (screw dowel rods to a 1 x 4, place styrofoam heads on dowels, attach board to wall using long shelf brackets).

Yep what MsPuppet said.

I've used hair spray on my puppets and it seems to work well for me, especially the beard on my devil puppet.