diff --git a/src/IntAna/IntAna_QuadQuadGeo.cxx b/src/IntAna/IntAna_QuadQuadGeo.cxx
index fb9a876959..bd4419cc87 100644
--- a/src/IntAna/IntAna_QuadQuadGeo.cxx
+++ b/src/IntAna/IntAna_QuadQuadGeo.cxx
@@ -118,8 +118,8 @@ class AxeOperator {
 //=======================================================================
 AxeOperator::AxeOperator(const gp_Ax1& A1,const gp_Ax1& A2) 
 {
-  myEPSILON_DISTANCE=0.00000000000001;
-  myEPSILON_AXES_PARA=0.000000000001;
+  myEPSILON_DISTANCE=1.0e-14;
+  myEPSILON_AXES_PARA=Precision::Angular();
   Axe1=A1; 
   Axe2=A2;
   //---------------------------------------------------------------------
@@ -268,12 +268,12 @@ IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(void)
 //=======================================================================
 void IntAna_QuadQuadGeo::InitTolerances()
 {
-  myEPSILON_DISTANCE               = 0.00000000000001;
-  myEPSILON_ANGLE_CONE             = 0.000000000001;
-  myEPSILON_MINI_CIRCLE_RADIUS     = 0.000000001;
-  myEPSILON_CYLINDER_DELTA_RADIUS  = 0.0000000000001;
-  myEPSILON_CYLINDER_DELTA_DISTANCE= 0.0000001;
-  myEPSILON_AXES_PARA              = 0.000000000001;
+  myEPSILON_DISTANCE               = 1.0e-14;
+  myEPSILON_ANGLE_CONE             = Precision::Angular();
+  myEPSILON_MINI_CIRCLE_RADIUS     = 0.01*Precision::Confusion();
+  myEPSILON_CYLINDER_DELTA_RADIUS  = 1.0e-13;
+  myEPSILON_CYLINDER_DELTA_DISTANCE= Precision::Confusion();
+  myEPSILON_AXES_PARA              = Precision::Angular();
 }
 //=======================================================================
 //function : IntAna_QuadQuadGeo
diff --git a/src/IntPatch/IntPatch_ImpImpIntersection_4.gxx b/src/IntPatch/IntPatch_ImpImpIntersection_4.gxx
index 377d8c2326..fed0712d74 100644
--- a/src/IntPatch/IntPatch_ImpImpIntersection_4.gxx
+++ b/src/IntPatch/IntPatch_ImpImpIntersection_4.gxx
@@ -1022,7 +1022,13 @@ stCoeffsValue::stCoeffsValue( const gp_Cylinder& theCyl1,
     }
   }
 
-  if(Abs(aDetV1V2) < aNulValue)
+  // In point of fact, every determinant (aDelta1, aDelta2 and aDelta3) is
+  // cross-product between directions (i.e. sine of angle).
+  // If sine is too small then sine is (approx.) equal to angle itself.
+  // Therefore, in this case we should compare sine with angular tolerance. 
+  // This constant is used for check if axes are parallel (see constructor
+  // AxeOperator::AxeOperator(...) in IntAna_QuadQuadGeo.cxx file).
+  if(Abs(aDetV1V2) < Precision::Angular())
   {
     Standard_Failure::Raise("Error. Exception in divide by zerro (IntCyCyTrim)!!!!");
   }
diff --git a/tests/bugs/moddata_3/bug26884 b/tests/bugs/moddata_3/bug26884
new file mode 100644
index 0000000000..6bb33bb3d9
--- /dev/null
+++ b/tests/bugs/moddata_3/bug26884
@@ -0,0 +1,34 @@
+puts "================"
+puts "OCC26884"
+puts "================"
+puts ""
+##############################################################
+# Cylinder/Cylinder intersection algorithm throws an exception
+##############################################################
+
+set max_time 0.1
+
+restore [locate_data_file bug26884-f1.brep] f1
+restore [locate_data_file bug26884-f2.brep] f2
+
+dchrono cr reset
+dchrono cr start
+
+set info [bopcurves f1 f2 -2d]
+
+dchrono cr stop
+
+if {![regexp {has no 3d curves} $info] ||
+    ![regexp {has no 3d points} $info] } {
+  puts "Error: wrong output"
+}
+
+set logTime [dchrono cr show]
+
+regexp {CPU user time: ([-0-9.+eE]+) seconds} $logTime full z
+
+if { $z > ${max_time} } {
+    puts "Elapsed time ($z) is more than ${max_time} seconds - Error"
+} else {
+    puts "Elapsed time ($z) is less than ${max_time} seconds - OK"
+}