Several examples of instabilities related to the capillary effects during nanocontacts are studied. For the single-asperity contact, there is a significant negative Laplace pressure inside water capillary bridges and the bridge may become unstable with respect to the phase transition, leading to an unstable capillary force. For the contact of two rough solid surfaces, the capillary force is also unstable with respect to small variations of roughness. For liquid in contact with a rough solid surface, the composite interface, which is required for the superhydrophobicity, can be destabilized and transformed into the homogeneous interface. Numerous examples show that the instabilities play an important role in nanocontact problems that involve capillarity.