In this paper we consider the construction of implicit second derivative Runge-Kutta collocation methods designed for the continuous numerical solution of stiff systems of first order initial value problems in ordinary differential equations. These methods are obtained based on the multistep collocation technique, which are shown to be convergent, with improved regions of absolute stability. Although the implementation of the second derivative Runge-Kutta collocation methods remains iterative due to the implicit nature of the methods, the advantage gained makes them suitable for solving stiff systems with eigenvalues of large modulus lying close to the imaginary axis. Some absolute stability characteristics and order of accuracy of the methods are studied. Finally, we show two possible ways of implementing the methods and compare them on some numerical examples found in the literature to demonstrate the high order of accuracy and reliability of the methods.