  In regression applications, the presence of nonlinearity and correlation
among observations offer computational challenges not only in traditional
settings such as least squares regression, but also (and especially) when the
objective function is non-smooth as in the case of quantile regression. In this
paper, we develop methods for the modeling and estimation of nonlinear
conditional quantile functions when data are clustered within two-level nested
designs. This work represents an extension of the linear quantile mixed models
of Geraci and Bottai (2014, Statistics and Computing). We develop a novel
algorithm which is a blend of a smoothing algorithm for quantile regression and
a second order Laplacian approximation for nonlinear mixed models. To assess
the proposed methods, we present a simulation study and two applications, one
in pharmacokinetics and one related to growth curve modeling in agriculture.
