  We identify contact transformations which linearize the given equations in
the Riccati and Abel chains of nonlinear scalar and coupled ordinary
differential equations to the same order. The identified contact
transformations are not of Cole-Hopf type and are \emph {new} to the
literature. The linearization of Abel chain of equations is also demonstrated
explicitly for the first time. The contact transformations can be utilized to
derive dynamical symmetries of the associated nonlinear ODEs. The wider
applicability of identifying this type of contact transformations and the
method of deriving dynamical symmetries by using them is illustrated through
two dimensional generalizations of the Riccati and Abel chains as well.
