I can see why someone would think there was Terrier, but I'm not so sure about Basenji. (The only way to know for sure is to do a DNA test.) Both of your dogs look very similar. What breed, or mix, is the older one?
Hey okay so this is wild but I figured I wanted to reach out! So I rescued my pup and his siblings from Puerto Rico after hurricane Maria and we have always wondered his breed. We know his mom is a chihuahua mix but it wasn’t until today that I realized he might be mixed with Basenji. I came across your post because we were trying to see if Basenji’s were even in PR. Do you know what city your little guy was picked up in?
OMG soooo cute. Her colouring and face don't look like a basenji, but maybe she's mixed with something with stronger genes. Do a DNA test. That would be fun!
The traits you described are also found in most of the Nordic/spitz type dogs. I don't see anything overly basenji-ish about him in the pics. What ever he is, he's very hansome.
Look at the BRAT mixes:
http://basenjirescue.org/DOGS-MIXES/Default.htm
Check out Tia. I think that's what you are looking for. :)
Then look at Tyson and Shiloh. Not the right coloring, but similar build and coat….
