The paper presents a Sugeno Adaptive Neuro-Fuzzy Inference System with parametric conjunction operations architecture, ANFIS-CX. The advantages of using parametric conjunction operations in fuzzy models are discussed, and learning rules for system identification with such operations are proposed. These learning strategies can include steepest descent gradient, differential evolution and least square estimation algorithms for tuning antecedent, conjunction, and consequent parameters, respectively. The results of system identification by parameter tuning of conjunction operations in addition to or instead of parameter tuning of the input membership functions are presented. Simulation results show that parameter training in conjunction operations, composed of four basic t-norms, significantly improves the approximation capability of fuzzy models.