When two material surfaces are brought into contact, the classical Amonton’s law predicts a monotonically increasing relation between the frictional force and the normal pressure. An abnormal friction law refers to the case where the friction force declines as the normal pressure increases. We investigate the possibility of abnormal tribological behavior for two surfaces coated with aligned multiwalled nanotube rafts. Part I of the investigation is devoted to the case when two contacting nanotube rafts are aligned to each other, while part II is aimed at more general case of arbitrarily oriented nanotube rafts. The analysis in part I is based on the JKR theory of adhesion and linear elasticity for aligned multiwalled carbon nanotube raft configuration. It gives rise of several interesting predictions. First, two surfaces covered by aligned nanotubes can adhere when bringing into a pressureless contact. Second, the aligned multiwalled nanotube rafts exhibit a detachment work that declines with the contacting pressure. Third, in contrast to the Amonton’s law, the frictional force would decline as the normal pressure increases.