Like many others, the feud between Ulrich von Gladwitz and Georg Znaeym has been inherited from ancestors, and the lines of demarcation are so ambiguous that there is no resolution to this generations' argument over a tract of land. Here is how the narrator describes this feud as Gradwitz patrols the dark forest:

A famous law suit, in the days of his grandfather, had wrested it from the illegal possession of a neighbouring family of petty landowners; the dispossessed party had never acquiesced in the judgment of the Courts, and a long series of poaching affrays and similar scandals had embittered the relationships between the families for three generations.

In other words, Gradwitz's grandfather had gone to court to "wrest" this land away from Znaeym's grandfather; however, the Znaeyms did not acknowledge the ruling of the court. So, now each family insists that the land is theirs, and they continue to hunt upon it. Resentment between the two parties waxes and the hatred becomes personal between Gradwitz and Znaeym so that the feud is aggrandized. This is why Gradwitz hopes one night that he can singularly come upon his enemy and kill him. But, just as comes around a tree, he comes vis-à-vis with Znaeym. Fatefully, however, in that "long silent moment" in which two civilized men cannot just shoot down someone down, a great tree splits in the storm and branches crash upon them. And, while they are thus pinioned beneath the tree and wait for their men to rescue them, it is only then that they put this feud into true perspective. 

The answer to this question can be found in the second paragraph of “The Interlopers.”  The feud between the Gradwitz and the Znaeym families started when there was a lawsuit between the two families in the time of the grandfathers of the two men who will figure prominently in this story.

The beginning of the story tells us that the Gradwitz family has a large amount of land that is very good for hunting.  However, on the night that the story takes place, Ulrich von Gradwitz is out patrolling a bit of land on the very edge of his property.  This piece of land is not really all that valuable for hunting, but he still values it above any other because of its role in this feud.

The narrator tells us that

A famous law suit, in the days of his grandfather, had wrested it from the illegal possession of a neighbouring family of petty landowners…

This family was the Znaeym family.  After the law suit, they did not accept the judgement and continued to believe that the land was theirs.  Over the years, there were many “poaching affrays and similar scandals” that had made the families hate one another even more.  This shows us that the feud in this story started out because of a law suit that had occurred in the time of Ulrich von Gradwitz’s grandfather.

Describe the feud between Ulrich Von Gradwitz's and Georg Znaeym's families in "The Interlopers."

The feud begins with a dispute over land ownership. Ulrich's grandfather, in a "famous law suit," won back the land illegally possessed by Georg's ancestors. Georg's family did not agree with the court's ruling and retaliated with "a long series of poaching affrays and similar scandals" which "had embittered the relationships between the families for three generations." 

Compounding this running feud was the fact that Georg and Ulrich hated each other since they were boys. The legal dispute became a personal feud as well. The story begins with Ulrich patrolling his lands waiting to catch Georg poaching. When the tree falls on them, their hate for each other is as strong as ever. Ulrich claims that if his men arrive first, he will be freed and Georg will die. Georg says the same. When Ulrich offers wine to Georg, Georg refuses. The feud is so strong that the two would rather hate than help each other even as they are in the same predicament. 

However, Ulrich has a change of heart and promises to free Georg first if his men are the first to arrive. After considering this gesture, Georg reciprocates and the feud is over. This occurs shortly before what would appear to be a gruesome end. 

What is the feud between Ulrich von Gladwitz's and Georg Znaeym's families?

The families of Ulrich von Gladwitz and Georg Znaeym have been engaged in a bitter feud for generations. Their beef relates to an old land dispute whose precise details have been lost in the mists of time. But however it started, this epic conflict has raged down through the years, passed on from generation to generation, each one more determined than the last to uphold their families' honor.

Now you might think that such a serious dispute could only possibly arise over a substantial piece of land, a valuable plot with extensive game and fish, or even perhaps large mineral deposits. But no. The land in question is nothing more than a narrow strip of woodland. Yet this small plot of land is enough to form the basis for a seemingly never-ending conflict between two warring families. This piece of "precipitous woodland" has become a symbol of family pride. After several generations of feuding it's no longer the land itself that's important but the principle it represents.