Summary of Law: No person may possess bears, cougars, or non-human primates as "pets." If you possessed one of these animals prior to the passage of the regulation you are grandfathered in.

Citation: LA. ADMIN. CODE tit. 76, §115
 
Following Information Contributed by caninesrock (Member of Sybils Message Board)
Lousiana Law

In Louisiana it is illegal to have:

a. Black bear (Ursus americanus);
b. Grizzly bear (Ursus arctos);
c. Polar bear (Ursus maritimus);
d. Red wolf (Canis rufus);
e. Gray wolf (Canis lupus);
f. Wolf dog hybrid (Canis lupus or Canis rufus x Canis familiarus);
g. All non-human primates;

h.The following big exotic cats:
i.Tigers;
ii.Lions;
iii.Leopards (including, but not limited to Snow Leopard and Clouded Leopard);
iv.Jaguars;
v.Cheetahs;
vi.Cougars or mountain lions (Felis concolor);
vii.All subspecies of the above listed exotic cats;
viii.Hybrids resulting from cross breeding of the above listed exotic cats

D. 1. Wolf-Dog Hybrids. The prohibition against wolfdog hybrids expired January 1, 1997. Persons are cautioned that local ordinances or other state regulations may prohibit possession of these animals. Any animal which appears indistinguishable from a wolf, or is in any way represented to be a wolf shall be considered to be a wolf in the absence of bona fide documentation to the contrary.

Baton Rouge and East Baton Rouge Parish,Caddo Parish, Rayne,Slidell,and Vivian make owning any kind of exotic pet illegal.