diff --git a/src/IntPatch/IntPatch_ImpImpIntersection_2.gxx b/src/IntPatch/IntPatch_ImpImpIntersection_2.gxx
index f94f8096d2..b1d3dfcbfd 100644
--- a/src/IntPatch/IntPatch_ImpImpIntersection_2.gxx
+++ b/src/IntPatch/IntPatch_ImpImpIntersection_2.gxx
@@ -177,8 +177,11 @@ void IntPatch_ImpImpIntersection::Perform(const Handle(Adaptor3d_HSurface)&  S1,
           aBox2.Add(gp_Pnt2d(aU2f, S2->FirstVParameter()));
           aBox2.Add(gp_Pnt2d(aU2l, S2->LastVParameter()));
 
-          const Standard_Real a2DTol = Min( S1->UResolution(TolTang),
-                                              S2->UResolution(TolTang));
+          // Resolution is too big if the cylinder radius is
+          // too small. Therefore, we shall bounde its value above. 
+          // Here, we use simple constant.
+          const Standard_Real a2DTol = Min(1.0e-4, Min( S1->UResolution(TolTang),
+                                              S2->UResolution(TolTang)));
 
           Standard_Boolean isReversed = ((aU2l - aU2f) < (aU1l - aU1f));
 
diff --git a/tests/bugs/modalg_6/bug27310_2 b/tests/bugs/modalg_6/bug27310_2
index 30e5754f8d..fe5faee133 100644
--- a/tests/bugs/modalg_6/bug27310_2
+++ b/tests/bugs/modalg_6/bug27310_2
@@ -6,7 +6,7 @@ puts ""
 # Huge tolerance obtained in the result of intersection of two cylindrical faces
 #################################################
 
-set ExpTol 7.7015195151142059e-006
+set ExpTol 0.00027580830315682321
 set GoodNbCurv 2
 
 restore [locate_data_file OCC496a.brep] a 
diff --git a/tests/bugs/modalg_6/bug27761 b/tests/bugs/modalg_6/bug27761
index 68222063ea..4b5c54f866 100644
--- a/tests/bugs/modalg_6/bug27761
+++ b/tests/bugs/modalg_6/bug27761
@@ -1,6 +1,3 @@
-puts "TODO OCC27766 ALL: Error : The command is not valid. The length is 0."
-puts "TODO OCC27766 ALL: Error : The length of result shape is"
-
 puts "========"
 puts "OCC27761"
 puts "========"
@@ -16,4 +13,16 @@ bsection result c1 c2
 
 checkshape result
 # approximate theoretical length of the result
-checkprops result -l 0.00201518
\ No newline at end of file
+checkprops result -l 0.00192624
+
+regexp {nb alone Vertices : ([-0-9.+eE]+)} [checksection result] full nbv
+if { $nbv != 0 } { puts "Error : Section is incorrect" }
+
+smallview
+don result
+fit
+clear
+disp c1 c2
+disp result
+
+checkview -screenshot -2d -path ${imagedir}/${test_image}.png
diff --git a/tests/bugs/modalg_6/bug27766 b/tests/bugs/modalg_6/bug27766
new file mode 100644
index 0000000000..d992b88ed2
--- /dev/null
+++ b/tests/bugs/modalg_6/bug27766
@@ -0,0 +1,30 @@
+puts "========"
+puts "OCC27766"
+puts "========"
+puts ""
+#################################################
+# Incorrect section curves between attached cylinders
+#################################################
+
+set ExpTol 1.0e-7
+set GoodNbCurv 5
+
+restore [locate_data_file bug27761_c1.brep] c1
+restore [locate_data_file bug27761_c2.brep] c2
+
+set log [bopcurves c1 c2 -2d]
+
+regexp {Tolerance Reached=+([-0-9.+eE]+)\n+([-0-9.+eE]+)} ${log} full Toler NbCurv
+
+if {${NbCurv} != ${GoodNbCurv}} {
+  puts "Error: Number of curves is bad!"
+}
+
+checkreal TolReached $Toler $ExpTol 0.0 0.1
+
+smallview
+don c_*
+fit
+disp c1 c2
+
+checkview -screenshot -2d -path ${imagedir}/${test_image}.png