We perform searches for gravitational-wave memory in the data of two major Pulsar Timing Array (PTA) experiments located in Europe and Australia. Supermassive black hole binaries (SMBHBs) are the primary sources of gravitational waves in PTA experiments. We develop and carry out the first search for late inspirals and mergers of these sources based on full numerical relativity waveforms with null (nonlinear) gravitational-wave memory. Additionally, we search for generic bursts of null gravitational-wave memory, exploring the possibilities of reducing the computational costs of these searches through kernel density estimation and normalizing flow approximations of the posteriors. We rule out mergers of SMBHBs with a chirp mass of 10(10)M(circle dot) up to 700 Mpc over 18 yr of observation at 95% credibility. We rule out the observation of generic displacement memory bursts with strain amplitudes >10(-14) in brief periods of observation time but across the sky, or over the whole observation time but for certain preferred sky positions, at 95% credibility.
