Emergent properties of complex adaptive systems (CAS) are explored by means of “agent-based modelling” (ABM), which are compared with results from modelling on the basis of the method of systems potential (MSP). MSP describes CAS as a holistic system whereas ABM-methodology considers CAS as set of interacting “agents.” It is argued that MSP is a “top-bottom” approach, which supplements ABM “bottom-up” modeling of CAS. Adaptive principles incorporated into CAS at the level of a holistic system exploit Lamarck’s ideas about evolution, while the adaptive rules incorporated in the inner structure of CAS reflect Darwin’s ideas. Both ABM and MSP exhibit the same macroscopic properties: (1) “punctuated equilibrium”; (2) sudden jumps in macro-indices; (3) cyclical dynamics; (4) superposition of deterministic and stochastic patterns in dynamics; (5) fractal properties of structure and dynamics; (6) SOC-phenomenon. ABM demonstrates these properties via simulations of the different models whereas MSP derives these phenomena analytically.