  Young planets offer a direct view of the formation and evolution processes
that produced the diverse population of mature exoplanet systems known today.
The repurposed Kepler mission K2 is providing the first sample of young
transiting planets by observing populations of stars in nearby, young clusters
or stellar associations. We report the detection and confirmation of two
planets transiting K2-264, an M2.5 dwarf in the 650 Myr old Praesepe open
cluster. Using our notch-filter search method on the K2 lightcurve, we identify
planets with periods of 5.84 d and 19.66 d. This is currently the second known
multi-transit system in open clusters younger than 1 Gyr. The inner planet has
a radius of 2.27$_{-0.16}^{+0.20}$ R$_\oplus$ and the outer planet has a radius
of 2.77$_{-0.18}^{+0.20}$ R$_\oplus$. Both planets are likely mini-Neptunes.
These planets are expected to produce radial velocity signals of 3.4 and 2.7
m/s respectively, which is smaller than the expected stellar variability in the
optical ($\simeq$30 m/s), making mass measurements unlikely in the optical, but
possible with future near-infrared spectrographs. We use an injection-recovery
test to place robust limits on additional planets in the system, and find that
planets larger than 2 R$_\oplus$ with periods of 1-20 d are unlikely.
