Archaic reflexes are reflexes, or involuntary automatic movements. The persistence of reflexes beyond a certain age can be a sign of a developmental disorder. Primary reflexes are primarily controlled by the brain stem since at birth, the maturation of the central nervous system remains incomplete and the myelination present is initially in the subcortical pathways. Subsequently, this myelination will reach the cortico-spinal pathways (cerebral cortex) which will ensure the progressive integration of the primary reflexes and the voluntary control of movements. A developmental disorder or injury to the nervous system (e.g. cerebral palsy, head trauma, stroke, dementia, etc.) can lead to the persistence or re-emergence of primary reflexes, as well as the disruption of the acquisition of motor control and postural reactions that influence the person's level of functioning and autonomy in daily activities (source: wikipedia, see wikipedia fact sheet for more details on reflexes).
 
There are several methods of reflex integration (RMTi, MNRI, IMP in particular).

Rhythmic Movement Training Integration (RMTi)
The RMTi was developed in the 1970s by Kerstin Linde, a Swedish movement specialist who works with children and adults with neurological problems. She studied the role of spontaneous movement in babies at different stages of development from the in-utero period and during the first year of life. 
Dr. Harald Blomberg, a Swedish psychiatrist, then went on to further study the role of movement in development, and the consequences for learning, emotions and behaviour. Moira Dempsey, who specializes in education and movement, and Dr. Blomberg formalized the method in a book on RMT®: "Movements that Heal".

Masgutova Neurosensorimotor Reflex Integration (MNRI) 
The MNRI® method was developed by Dr. Svetlana Masgutova, who has been conducting research on primary movements and their influence on development and learning since 1989.
Her work focuses on the concepts of development and integration of archaic reflexes in order to restore the neurosensory-motor process, facilitate learning and develop emotional balance.

Primary Motor Integration (PMI) 
IMP allows the identification and integration of non-integrated reflexes and reactions using simple and easy to practice movements and remodelling procedures alone or with a partner. 
The effect may be visible at different levels (physical: coordination and posture; cognitive: learning and reflection; emotional, relational...).
IMP was born from the synthesis of different approaches, including Brain gym and other methods for children with DYS disorders in particular.