Conditions for the emergence of a statistical relationship between T_r, the chaotic transport (recurrence) time, and T_L, the local Lyapunov time (the inverse of the numerically measured largest Lyapunov characteristic exponent), are considered for the motion inside the chaotic layer around the separatrix of a nonlinear resonance. When numeric values of the Lyapunov exponents are measured on a time interval not greater than T_r, the relationship is shown to resemble the quadratic one. This tentatively explains numeric results presented in the literature.