  The dynamics of an ensemble of $N$ weakly coupled limit-cycle oscillators can
be captured by their $N$ phases using standard phase reduction techniques.
However, it is a phenomenological fact that all-to-all strongly coupled
limit-cycle oscillators may behave as "quasiphase oscillators", evidencing the
need of novel reduction strategies. We introduce here quasi phase reduction
(QPR), a scheme suited for identical oscillators with polar symmetry
($\lambda-\omega$ systems). By applying QPR we achieve a reduction to $N+2$
degrees of freedom: $N$ phase oscillators interacting through one independent
complex variable. This "quasi phase model" is asymptotically valid in the
neighborhood of incoherent states, irrespective of the coupling strength. The
effectiveness of QPR is illustrated in a particular case, an ensemble of
Stuart-Landau oscillators, obtaining exact stability boundaries of uniform and
nonuniform incoherent states for a variety of couplings. An extension of QPR
beyond the neighborhood of incoherence is also explored. Finally, a general QPR
model with $N+2M$ degrees of freedom is obtained for coupling through the first
$M$ harmonics.
