  In this paper we study application of Le Cam's one-step method to parameter
estimation in ordinary differential equations models. This computationally
simple technique can serve as an alternative to numerical evaluation of the
popular nonlinear least squares estimator, which typically requires the use of
a multi-step iterative algorithm and repetitive numerical integration of the
ODE system. The one-step method starts from a preliminary $\sqrt{n}$-consistent
estimator of the parameter of interest and next turns it into an asymptotic (as
the sample size $n\rightarrow\infty$) equivalent of the least squares estimator
through a numerically straightforward procedure. We demonstrate performance of
the one-step estimator via extensive simulations and real data examples. The
method enables the researcher to obtain both point and interval estimates. The
preliminary $\sqrt{n}$-consistent estimator that we use depends on
nonparametric smoothing, and we provide a data driven methodology for choosing
its tuning parameter and support it by theory. An easy implementation scheme of
the one-step method for practical use is pointed out.
