  Phase reduction is a general approach to describe coupled oscillatory units
in terms of their phases, assuming that the amplitudes are enslaved. For such a
reduction, the coupling should be small, but one also expects the reduction to
be valid for finite coupling. This paper presents a general framework allowing
us to obtain coupling terms in higher orders of the coupling parameter for
generic two-dimensional oscillators and arbitrary coupling terms. The theory is
illustrated with an accurate prediction of Arnold's tongue for the van der Pol
oscillator exploiting higher-order phase reduction.
