Novel computing technologies that imitate the principles of biological neural systems may offer low power consumption along with distinct cognitive and learning advantages. The development of reliable memristive devices capable of storing multiple states of information has opened up new applications such as neuromorphic circuits and adaptive systems. At the same time, the explosive growth of the printed electronics industry has expedited the search for advanced memory materials suitable for manufacturing flexible devices. Here, we demonstrate that solution-processed MoOx/MoS2 and WOx/WS2 heterostructures sandwiched between two printed silver electrodes exhibit an unprecedentedly large and tunable electrical resistance range from 10(2) to 10(8) Ω combined with low programming voltages of 0.1-0.2 V. The bipolar resistive switching, with a concurrent capacitive contribution, is governed by an ultrathin (<3 nm) oxide layer. With strong nonlinearity in switching dynamics, different mechanisms of synaptic plasticity are implemented by applying a sequence of electrical pulses.