The concept of lumped optical nanoelements (or metactronics), wherein nanometer-scale structures act as nanoinductors, nanocapacitors and nanoresistors, has attracted a great deal of attention as a simple toolbox for engineering different nanophotonic devices in analogy with microelectronics. While recent studies of the topic have been predominantly focused on linear functionalities, nonlinear dynamics in microelectronic devices plays a crucial role and provides a majority of functions, employed in modern applications. Here, we extend the metactronics paradigm and add nonlinear dynamical modalities to those nanophotonic devices that have never been associated with optical nanoantennas. Specifically, we show that nonlinear dimer nanoantennae can operate in the regimes of tristable and astable multivibrators as well as chaos generators. The physical mechanism behind these modalities relies on the Kerr-type nonlinearity of nanoparticles in the dimer enhanced by a dipolar localized surface plasmon resonance. This allows one to provide a positive nonlinear feedback at moderate optical intensities, leading to the desired dynamical behavior via tuning the driving field parameters. Our findings shed light on a novel class of nonlinear nanophotonic devices with a tunable nonlinear dynamical response.