The program ABC NDC is universal tool for investigation typical nonlinear dynamical systems which can be governed by ODE (dimension D = 3) or by discrete-time equations (dimension d = 2). The program ABC NDC is the second improved and extended version of the program NLO [1]. Methods and algorithms used in ABC NDC are discussed and illustrated on concrete dynamical systems with different strong nonlinearity, such as polynomial, piecewise linear and impact. Some new and original approaches are used in the program – line and contour mapping, building of periodic skeleton, calculation of complete bifurcation diagrams with stable and unstable orbits, one-parameter diagrams, dynamical characteristics, backbone curves, following stable and unstable solutions. All problems, methods and approaches worked out in literature on bifurcation theory and nonlinear dynamics and chaos, for example [2] may be realized in the program as well. ABC NDC allows to investigate many different nonlinear dynamical models that have great importance for applications in technology and scientific disciplines like mechanics, physics, chemistry, electrodynamics, biology, etc. ABC NDC has friendly and intuitive user interface and no requires programming skills. The goal of ABC NDC is create the rather universal software for both the professional scientists and interested non-scientist or student. The program is purposed for ungraduate students, postgraduate and PhD students, for engineers and scientists, which are interesting in the problem of Nonlinear Dynamics and Chaos, nonlinear oscillations, ODE and discrete-time difference equations.