  We present a system of $N$-coupled Li\'enard type nonlinear oscillators which
is completely integrable and possesses explicit $N$ time-independent and $N$
time-dependent integrals. In a special case, it becomes maximally
superintegrable and admits $(2N-1)$ time-independent integrals. The results are
illustrated for the N=2 and arbitrary number cases. General explicit periodic
(with frequency independent of amplitude) and quasiperiodic solutions as well
as decaying type/frontlike solutions are presented, depending on the signs and
magnitudes of the system parameters. Though the system is of a nonlinear damped
type, our investigations show that it possesses a Hamiltonian structure and
that under a contact transformation it is transformable to a system of
uncoupled harmonic oscillators.
