After arriving in the United States in 1969, Swami Rama began teaching Hatha yoga at the YMCA and in private homes. He was concerned that the YMCA presented yoga solely as a physical fitness program, so he included philosophy and meditation in his classes. In 1971, he founded the Himalayan Institute of Yoga Science and Philosophy in Glenview, Illinois. The headquarters of the institute was later moved to Honesdale, Pennsylvania, which was purchased in 1977. The institute now has branches in the United States, Europe, and India. Swami Rama also founded other teaching and service organizations, including a large medical facility in Dehradun in Uttarakhand, India, to serve millions of poor people in the nearby mountains who had little access to health care.
Swami Rama was known for his ability to control his body during yoga nidra, a guided meditation that means "yogic sleep." His abilities in yoga nidra were experimentally measured at the Menninger Foundation in Topeka, Kansas, in 1971. He was able to produce different brain waves at will and stay aware throughout the meditation. In another experiment at the Menninger Foundation, he voluntarily stopped his heart from pumping blood for 17 seconds. He also created a temperature differential of 5 degrees Celsius between two areas on the palm of his right hand. These psychosomatic states gained him widespread attention in the media, and he acquired a reputation for achieving remarkable feats of autonomic control. However, he criticized the tendency for yogis to use supernatural feats to demonstrate their enlightenment, arguing that these only demonstrated the ability to perform a feat.