  The spectral distance for noncommutative Moyal planes is considered in the
framework of a non compact spectral triple recently proposed as a possible
noncommutative analog of non compact Riemannian spin manifold. An explicit
formula for the distance between any two elements of a particular class of pure
states can be determined. The corresponding result is discussed. The existence
of some pure states at infinite distance signals that the topology of the
spectral distance on the space of states is not the weak * topology. The case
of the noncommutative torus is also considered and a formula for the spectral
distance between some states is also obtained.
