The main law on drugs in Kenya, as far as I could find out, is the Narcotic Drugs and Psychotropic Substances Control Act, first adopted in 1994. Kenyalaw.org has a database containing all laws in Kenya, you can read the law online there. When I browsed it, it was unclear to me which drugs are exactly outlawed; next to cannabis (i.e. hash and weed) there was talk of "other narcotics and psychotropic substances" but does the law clearly define which ones they are?
