  Context. In the last five years the Fermi Large Area Telescope (LAT)
instrument detected GeV {\gamma}-ray emission from five novae. The GeV emission
can be interpreted in terms of an inverse Compton process of electrons
accelerated in a shock. In this case it is expected that protons in the same
conditions can be accelerated to much higher energies. Consequently they may
produce a second component in the {\gamma}-ray spectrum at TeV energies. Aims.
We aim to explore the very-high-energy domain to search for {\gamma}-ray
emission above 50 GeV and to shed light on the acceleration process of leptons
and hadrons in nova explosions. Methods. We have performed observations with
the MAGIC telescopes of the classical nova V339 Del shortly after the 2013
outburst, triggered by optical and subsequent GeV {\gamma}-ray detec- tions. We
also briefly report on VHE observations of the symbiotic nova YY Her and the
dwarf nova ASASSN-13ax. We complement the TeV MAGIC observations with the
analysis of con- temporaneous Fermi-LAT data of the sources. The TeV and GeV
observations are compared in order to evaluate the acceleration parameters for
leptons and hadrons. Results. No significant TeV emission was found from the
studied sources. We computed upper limits on the spectrum and night-by-night
flux. The combined GeV and TeV observations of V339 Del limit the ratio of
proton to electron luminosities to Lp<~0.15 Le.
