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The Nightmare Man was, at first, an immaterial being from another dimension. He was attracted to the universe by the mind of Luke Smith, which he planned to use to pull himself into the universe. He manifested himself in the universe through the nightmares of Luke Smith, using Luke's powerful mind and trapping Luke in the dream dimension.
Once in the universe, he placed Clyde and Rani in a nightmares and began to induce nightmares in the sleeping population to feed himself. When some of his power was cut off by Luke pulling Clyde and Rani out of their nightmares to join him, he went back to Sarah Jane's house and short-circuited K9 and Mr Smith. After almost being tricked by Sarah Jane to place her in a nightmare so she could join them, he travelled back to Luke's nightmare.
He tried to send Clyde and Rani back into their nightmares. He was defeated when Luke, Clyde and Rani shrugged off their fears and stood against him. As they didn't fear him, he lost his power over them and weakened. The Nightmare Man was imprisoned in a nightmare of his own, listening to his dream version of Sarah Jane Smith telling him how wonderful her son was for the rest of eternity. (TV: The Nightmare Man)
The Nightmare Man was sinister, masochistic, psychopathic, malevolent and cruel. He demonstrated incredible sadism, taunting Luke that all which was happening was Luke's fault. Displays of psychotic personality traits were his almost laid-back and carefree behavior, even in the face of people equal to him. This is also possibly the reason for his extreme narcissism.
Although the full extent of his capabilities are never truly explained, he is shown to be an extraordinarily powerful entity. The Nightmare Man was able to visit Luke in his nightmares, and draw power from nightmares. He was able to control others' dreams, and possess their minds, giving him limited control over them. With enough power, he could physically manifest himself into the universe. Once he had, he gained far greater powers. He could make those awake sleep and create nightmares in the minds of those already asleep, feeding off their fear. The range of his powers also greatly increased. He could have sent the whole world to sleep. He was also able to make beings having nightmares unwakeable
He could fire offensive energy blasts that damaged K9 and cause Mr Smith to short circuit by pointing at him. He could teleport around the real word and back into the dream world. He could control people while they were asleep, as long as they feared him. Those he created nightmares for might enter the same dream as others with intense concentration, which caused him pain.
As he fed off all nightmares that every man, woman and child ever had, he also knew all their nightmares and knew about everyone. His power to create nightmares was so great he could make Luke have nightmares, even though Luke did not otherwise dream. Even before he physically manifested himself, he could control dreams. Once he physically manifested, he could control more than one dream to the same level at once.