  We present an analysis of the X-ray time lags for the highly variable Seyfert
1 galaxy NGC 4051, based on a series of XMM-Newton observations taken in 2009.
We investigate the Fourier frequency dependent time lags in the light curves
between the 0.3--1.0 keV and 2.0--5.0 keV energy bands as a function of source
flux, including simultaneous modelling of the resulting lag-frequency spectra.
We find the shape of the lag-frequency spectra to vary significantly and
systematically with source flux. We model the lag-frequency spectra using
simple transfer functions, and find that two time lag components are required,
one in each energy band. The simplest acceptable fits have only the relative
contribution of the lagged component in the hard band varying with flux level,
which can be associated with changes in the energy spectrum. We discuss the
interpretation of these results in terms of the currently popular models for
X-ray time lags.
