  A search for nonresonant excesses in the invariant mass spectra of electron
and muon pairs is presented. The analysis is based on data from proton-proton
collisions at a center-of-mass energy of 13 TeV recorded by the CMS experiment
in 2016, corresponding to a total integrated luminosity of 36 fb$^{-1}$. No
significant deviation from the standard model is observed. Limits are set at
95% confidence level on energy scales for two general classes of nonresonant
models. For a class of fermion contact interaction models, lower limits ranging
from 20 to 32 TeV are set on the characteristic compositeness scale $\Lambda$.
For the Arkani-Hamed, Dimopoulos, and Dvali model of large extra dimensions,
the first results in the dilepton final state at 13 TeV are reported, and
values of the ultraviolet cutoff parameter $\Lambda_\mathrm{T}$ below 6.9 TeV
are excluded. A combination with recent CMS diphoton results improves this
exclusion to $\Lambda_\mathrm{T}$ below 7.7 TeV, providing the most sensitive
limits to date in nonhadronic final states.
