  This paper considers a type of generalized large $q$ SYK models which include
multi-body interactions between Majorana fermions. We derive an effective
action in the limit of large $N$ and large $q$ (with ${~q^2\over N} $ small),
and find a universal expression for thermodynamical quantities. We also
consider the chaos exponent using the retarded kernel method and find an
efficient way to calculate the Lyapunov exponent for generalized large $q$ SYK
models numerically.
