The Gebrüder Thonet company was founded in 1819 by Michael Thonet to produce his chairs using a unique process of bending wood ("bentwood") that he designed. The company is still in business today, run by the fifth generation of Thonets, with headquarters in Frankenberg, Germany. Although the company branched off into producing other types of chairs and furniture pieces, it is still best known for its bentwood wicker designs, the first of which appeared in 1860. These have remained remarkably consistent in style since their first appearance, but there are some clues you can use to determine the age of a particular bentwood rocker.
Familiarise yourself with the design of the first Thonet bentwood wicker rocker, the "Schaukel-Fauteuil No. 1" or "Rocking Chair No. 1." Produced in 1890 in Koritschan, Moravia, it was the first rocking chair in the world created from "bentwood," a technique Michael Thonet developed by wetting and bending beechwood. Check out a picture on the company website (thonet.de/en/rocking-chair.html).
Notice how the design of the curved legs and arms changed over the years. According to a visual history of the modern rocking chair created by Designboom, the legs on the Thonet wicker rockers began with quite simple curves and then got more elaborate over the years, becoming noticeably more curlicued around the turn of the 20th century. Both ends of the bottom runners on chairs of this period curved under as well, in contrast to the straight edges of previous versions. The arms of the first rocker sat lower than those of later versions, which were markedly rounder.
Look for manufacturing marks to authenticate your chair. There have been many reproductions and generic chairs called "bentwood rockers" through the years. A sure way of identifying a real Thonet from around the turn of the 20th century is the presence of the company name (THONET) with a solid line underneath carved somewhere into the chair. This mark could be on the bottom of the curved arms or legs or under the seat . A paper label with the company's name on it may also be present, though it may have come off over the years, so its absence does not prove you do not have a real Thonet.
Determine if you have a "new" collectable. In fall 2009, the Thonet company marked its sesquicentennial by producing a limited edition of chairs in the Thonet Collect series that replicated the famous "Rocking Chair No. 1." This collector's edition was limited to 25 pieces made of authentic beechwood and stained in one of three colours: black, hazelnut and mahogany. The rockers were constructed using traditional methods and original tools and, like the originals, the oval back and seat of the chair were made of solid cane work. Individual pieces from the Thonet Collect series were numbered and came with hand-signed certificates of authenticity (which may or not still be with your chair).
Consult an authoritative source and study the pictures to familiarise yourself with the different designs of different eras. The book, "Thonet Bentwood and Other Furniture: The 1904 Illustrated Catalogue," by Gebrüder and Michael Thonet describes the dimensions of these rockers, and illustrates their designs through the years. It states that some chairs had paper labels affixed with the Thonet company name on them. A new reproduction of this book was produced by Dover Publications in 1980, and is available through Amazon.com.