An illegal stamp is defined by the Universal Postal Union as a stamp that carries the name of a legitimate country or territory, but was not produced or printed by the postal administration of that country, and is not valid for postage anywhere in the world.
Following a 2004 ATA Board meeting the following was printed in Topical Time:
"Illegal" Stamps: Recognizing that stamp collectors are concerned over the increase in the distribution of "illegal" stamps as identified by the International Bureau of the Universal Postal Union, but also understanding that surveys taken by ATA, APS, and other philatelic organizations clearly point out that stamp collectors do not want to be told what to collect, the ATA Board adopted the following resolution:
To find out more about illegal issues you can access the following links:
ATA reaffirms it policies of 1954 and 1970 to inform and educate collectors about "illegal stamps." To do this, ATA shall include data provided by the International Bureau of the Universal Postal Union in Topical Time, and on the ATA website with links to other sites discussing this issue. However, ATA does not take a stand on what is or isn't "illegal," and on what topical collectors should or should not collect.
ATA member William Silvester wrote an excellent article that appears in the September-October 2016 issue of Topical Time. "Beware the Illegal Stamps" is found here.