Summary: In this paper we calculate the critical scaling exponents describing the variation of both the positive Lyapunov exponent, \( \lambda^+\), and the mean residence time, \( \langle \tau \rangle \), near the second order phase transition critical point for dynamical systems experiencing crisis-induced intermittency. We study in detail 2-dimensional 2-parameter nonlinear quadratic mappings of the form: \(X_{n+1} = f_1 (X_n, Y_n; A, B)\) and \(Y_{n+1} = f_2 (X_n, Y_n; A, B)\) which contain in their parameter space \((A, B)\) a region where there is crisis-induced intermittent behaviour. Specifically, the Henon, the Mira 1, and Mira 2 maps are investigated in the vicinity of the crises. We show that near a critical point the following scaling relations hold: \(\langle \tau \rangle \sim |A - A_c|^{- \gamma}\), \((\lambda^+ - \lambda_c^+) \sim |A - A_c|^{\beta_A}\) and \((\lambda^+ - \lambda_c^+) \sim |B - B_c|^{\beta_B}\). The subscript \(c\) on a quantity denotes its value at the critical point. All these maps exhibit a chaos to chaos second order phase transition across the critical point. We find these scaling exponents satisfy the scaling relation \(\gamma = \beta_B (\frac{1}{\beta_A} - 1)\), which is analogous to Widom’s scaling law. We find strong agreement between the scaling relationship and numerical results.