Given x(0) is an element of R-n we study the infinite-horizon problem of minimizing the expression integral(0)(T) f(x(t), x’(t))dt as T grows to infinity, where a function x : [0, infinity) --> R-n is absolutely continuous and satisfies the initial condition x(0) = x(0) and f = f(x,u) is an integrand. We study the structure of (f)-weakly optimal solutions and establish the turnpike property for a generic integrand f.