diff --git a/src/Extrema/Extrema_ExtCC.cxx b/src/Extrema/Extrema_ExtCC.cxx
index d6eb92a41c..def27cbe5e 100644
--- a/src/Extrema/Extrema_ExtCC.cxx
+++ b/src/Extrema/Extrema_ExtCC.cxx
@@ -602,6 +602,9 @@ void Extrema_ExtCC::PrepareParallelResult(const Standard_Real theUt11,
     const Bnd_Range aRange(theUt21, theUt22);
     Bnd_Range aProjRng1;
 
+    // Precision of the calculation depends on circles radii
+    const Standard_Real aPrecision = Max(Epsilon(myC[0]->Circle().Radius()), Epsilon(myC[1]->Circle().Radius()));
+
     // Project arc of the 1st circle between points theUt11 and theUt12 to the
     // 2nd circle. It is necessary to chose correct arc from two possible ones.
 
@@ -678,7 +681,7 @@ void Extrema_ExtCC::PrepareParallelResult(const Standard_Real theUt11,
           aMinSqD = Min(aMinSqD, ExtPCir.SquareDistance(anExtID));
         }
 
-        if (aMinSqD <= aMinSquareDist + (1. + aMinSqD) * Epsilon(1. + aMinSqD))
+        if (aMinSqD <= aMinSquareDist + (1. + aMinSqD) * aPrecision)
         {
           ClearSolutions();
           mySqDist.Append(aMinSqD);
@@ -778,7 +781,7 @@ void Extrema_ExtCC::PrepareParallelResult(const Standard_Real theUt11,
             imin = k;
           }
         }
-        if (aDmin <= aMinSquareDist + (1. + aDmin) * Epsilon(1. + aDmin))
+        if (aDmin <= aMinSquareDist + (1. + aDmin) * aPrecision)
         {
           if (imin == 0)
           {
diff --git a/tests/bugs/modalg_7/bug32874 b/tests/bugs/modalg_7/bug32874_1
similarity index 100%
rename from tests/bugs/modalg_7/bug32874
rename to tests/bugs/modalg_7/bug32874_1
diff --git a/tests/bugs/modalg_7/bug32874_2 b/tests/bugs/modalg_7/bug32874_2
new file mode 100644
index 0000000000..0ee16c9efa
--- /dev/null
+++ b/tests/bugs/modalg_7/bug32874_2
@@ -0,0 +1,29 @@
+puts "================================================="
+puts "0032874: IsParallel() method of Extrema_ExtCC does not give same results in OCC 7.6.0 vs OCC 7.5.0"
+puts "================================================="
+puts ""
+
+set distExpected 3.5
+circle c1 0 0 0 100
+circle c2 0 0 0 100+$distExpected
+
+set start {0.0 0.5*pi pi 1.5*pi 2.0*pi}
+set delta {pi/4.0 pi/3.0 pi/2.0 0.55*pi 0.99*pi pi 1.1*pi}
+
+foreach f $start {
+  foreach d $delta {
+    trim cc1 c1 $f $f+$d
+    trim cc2 c2 $f $f+$d
+
+    set extr [extrema cc1 cc2]
+    if {[regexp {Infinite number of extremas, distance = ([-0-9.+eE]+)} $extr full dist]} {
+      if {[expr abs($dist - $distExpected)] < 1.e-7} {
+        puts "OK"
+      } else {
+        puts "Error: wrong distance $dist instead of $distExpected expected"
+      }
+    } else {
+      puts "Error: non-parallel curves"
+    }
+  }
+}
diff --git a/tests/bugs/modalg_7/bug32874_3 b/tests/bugs/modalg_7/bug32874_3
new file mode 100644
index 0000000000..8ff06ca948
--- /dev/null
+++ b/tests/bugs/modalg_7/bug32874_3
@@ -0,0 +1,30 @@
+puts "================================================="
+puts "0032874: IsParallel() method of Extrema_ExtCC does not give same results in OCC 7.6.0 vs OCC 7.5.0"
+puts "================================================="
+puts ""
+
+set radius 0.001
+set distExpected 0.00001
+circle c1 0 0 0 $radius
+circle c2 0 0 0 $radius+$distExpected
+
+set start {0.0 0.5*pi pi 1.5*pi 2.0*pi}
+set delta {pi/4.0 pi/3.0 pi/2.0 0.55*pi 0.99*pi pi 1.1*pi}
+
+foreach f $start {
+  foreach d $delta {
+    trim cc1 c1 $f $f+$d
+    trim cc2 c2 $f $f+$d
+
+    set extr [extrema cc1 cc2]
+    if {[regexp {Infinite number of extremas, distance = ([-0-9.+eE]+)} $extr full dist]} {
+      if {[expr abs($dist - $distExpected)] < 1.e-7} {
+        puts "OK"
+      } else {
+        puts "Error: wrong distance $dist instead of $distExpected expected"
+      }
+    } else {
+      puts "Error: non-parallel curves"
+    }
+  }
+}
diff --git a/tests/bugs/modalg_7/bug32874_4 b/tests/bugs/modalg_7/bug32874_4
new file mode 100644
index 0000000000..9fc0988886
--- /dev/null
+++ b/tests/bugs/modalg_7/bug32874_4
@@ -0,0 +1,30 @@
+puts "================================================="
+puts "0032874: IsParallel() method of Extrema_ExtCC does not give same results in OCC 7.6.0 vs OCC 7.5.0"
+puts "================================================="
+puts ""
+
+set radius 0.001
+set distExpected 1000.0
+circle c1 0 0 0 $radius
+circle c2 0 0 0 $radius+$distExpected
+
+set start {0.0 0.5*pi pi 1.5*pi 2.0*pi}
+set delta {pi/4.0 pi/3.0 pi/2.0 0.55*pi 0.99*pi pi 1.1*pi}
+
+foreach f $start {
+  foreach d $delta {
+    trim cc1 c1 $f $f+$d
+    trim cc2 c2 $f $f+$d
+
+    set extr [extrema cc1 cc2]
+    if {[regexp {Infinite number of extremas, distance = ([-0-9.+eE]+)} $extr full dist]} {
+      if {[expr abs($dist - $distExpected)] < 1.e-7} {
+        puts "OK"
+      } else {
+        puts "Error: wrong distance $dist instead of $distExpected expected"
+      }
+    } else {
+      puts "Error: non-parallel curves"
+    }
+  }
+}
diff --git a/tests/bugs/modalg_7/bug32874_5 b/tests/bugs/modalg_7/bug32874_5
new file mode 100644
index 0000000000..4cb2e68340
--- /dev/null
+++ b/tests/bugs/modalg_7/bug32874_5
@@ -0,0 +1,30 @@
+puts "================================================="
+puts "0032874: IsParallel() method of Extrema_ExtCC does not give same results in OCC 7.6.0 vs OCC 7.5.0"
+puts "================================================="
+puts ""
+
+set radius 1000.0
+set distExpected 1.e-5
+circle c1 0 0 0 $radius
+circle c2 0 0 0 $radius-$distExpected
+
+set start {0.0 0.5*pi pi 1.5*pi 2.0*pi}
+set delta {pi/4.0 pi/3.0 pi/2.0 0.55*pi 0.99*pi pi 1.1*pi}
+
+foreach f $start {
+  foreach d $delta {
+    trim cc1 c1 $f $f+$d
+    trim cc2 c2 $f $f+$d
+
+    set extr [extrema cc1 cc2]
+    if {[regexp {Infinite number of extremas, distance = ([-0-9.+eE]+)} $extr full dist]} {
+      if {[expr abs($dist - $distExpected)] < 1.e-7} {
+        puts "OK"
+      } else {
+        puts "Error: wrong distance $dist instead of $distExpected expected"
+      }
+    } else {
+      puts "Error: non-parallel curves"
+    }
+  }
+}