Reconnection processes of twin-chains are systematically studied in the quadratic twist map. By using the reversibility and symmetry of the mapping, the location of the is theoretically determined in the phase space. The enable us to obtain useful information about the reconnect ion processes and the transition to global chaos. We succeed in deriving the general conditions for the reconnection thresholds. In addition, a new type of reconnect ion process which generates shearless curves is studied. In the past decades, enormous effort has been dedicated to the study of two dimensional area-preserving maps with the twist condition,l) but very few studies have been made of nontwist maps. Recent studies on nontwist maps have revealed that rich properties are generated by violating the twist condition. 2) - 6) In a previous paper, 6) we studied the properties of the quadratic twist map and numerically determined the critical boundary in the two-dimensional parame ter space, where the transition to global chaos occurs. The critical boundary has many sharp singular structures, and their locations seem to have a one-to-one corre spondence with those of the reconnect ion thresholds. The relationship between the transition to global chaos and the reconnect ion processes was first pointed out by Howard and Hohs,2) but it has not yet been thoroughly investigated. In order to investigate the detailed structure of the critical boundary, one needs accurate information regarding the reconnection processes. In this paper, we study the details of the reconnect ion processes in the quadratie twist map and propose a theoretieal method to determine the reconnection thresholds. We show that the reversibility and symmetry of the mapping guarantee the existence of the indicator points in the phase space. These enable us to study the reconnect ion processes sys tematieally. For twin-chains of period one and period two, the reconnect ion thresh olds have already been determined, either exactly or approximately. 2), 3) The method presented here reproduces results which have been previously obtained, and it pro vides general conditions for the reconnect ion thresholds. The quadratie twist map (QTM) is defined by