  The next-generation Event Horizon Telescope (ngEHT) will be a significant
enhancement of the Event Horizon Telescope (EHT) array, with $\sim 10$ new
antennas and instrumental upgrades of existing antennas. The increased
$uv$-coverage, sensitivity, and frequency coverage allow a wide range of new
science opportunities to be explored. The ngEHT Analysis Challenges have been
launched to inform development of the ngEHT array design, science objectives,
and analysis pathways. For each challenge, synthetic EHT and ngEHT datasets are
generated from theoretical source models and released to the challenge
participants, who analyze the datasets using image reconstruction and other
methods. The submitted analysis results are evaluated with quantitative
metrics. In this work, we report on the first two ngEHT Analysis Challenges.
These have focused on static and dynamical models of M87* and Sgr A*, and shown
that high-quality movies of the extended jet structure of M87* and near-horizon
hourly timescale variability of Sgr A* can be reconstructed by the reference
ngEHT array in realistic observing conditions, using current analysis
algorithms. We identify areas where there is still room for improvement of
these algorithms and analysis strategies. Other science cases and arrays will
be explored in future challenges.
