According to a spokesperson from Motorola, the Android 7.0 Nougat software update is coming to the family of Moto Z devices as well as the Moto G4 before the end of the year. While the spokesperson mentions that Q4 will be the time that users of these devices can expect to see Android 7.0 come to their phones, Q4 is the only detail mentioned in reference to the time frame as no exact dates were given for any of the devices which belong to the most recent crop of Moto offerings in the smartphone market. That said, the fourth quarter of the year starts in October so it's quite possible that any of these devices could start seeing over-the-air updates to Android Nougat within the next couple of weeks.
It wasn't stated which Moto devices are set to get the update to Nougat first, although given the Moto G4 has been out longer it would seem logical to push the software to this device before the Moto Z family of smartphones. Having said that, the Moto Z family of devices are the flagships, so it could really go either way. For those that are curious and will want to stay on top of checking whether or not their devices are ready for an update, Motorola's software support page will be listing the details for the status of each phone that is going to be supported by Android Nougat, so that will be a useful resource to keep handy. If you're not too worried about the update, you can simply wait for the alert to hit your device that a new update is available for download.
In regards to the phones mentioned here, the Moto Z, Moto Z Force, and Moto Z Play, as well as the Moto G4 and the Moto G4 Plus will all be getting the update to Nougat sometime in the near future. Beyond these devices, there is currently no detail on when other past Moto phones will be getting the bump to the next version of Android. When the updates are released, Moto Z and Moto G4 owners can expect things like improved Doze Mode, multi-window support, and more.