diff --git a/hist/hist/src/TAxis.cxx b/hist/hist/src/TAxis.cxx
index 641c09edb602c..49ea43db92a0b 100644
--- a/hist/hist/src/TAxis.cxx
+++ b/hist/hist/src/TAxis.cxx
@@ -800,7 +800,7 @@ void TAxis::Set(Int_t nbins, const Float_t *xbins)
    for (bin=0; bin<= fNbins; bin++)
       fXbins.fArray[bin] = xbins[bin];
    for (bin=1; bin<= fNbins; bin++)
-      if (fXbins.fArray[bin] < fXbins.fArray[bin-1])
+      if (fXbins.fArray[bin] <= fXbins.fArray[bin - 1])
          Error("TAxis::Set", "bins must be in increasing order");
    fXmin      = fXbins.fArray[0];
    fXmax      = fXbins.fArray[fNbins];
@@ -818,7 +818,7 @@ void TAxis::Set(Int_t nbins, const Double_t *xbins)
    for (bin=0; bin<= fNbins; bin++)
       fXbins.fArray[bin] = xbins[bin];
    for (bin=1; bin<= fNbins; bin++)
-      if (fXbins.fArray[bin] < fXbins.fArray[bin-1])
+      if (fXbins.fArray[bin] <= fXbins.fArray[bin - 1])
          Error("TAxis::Set", "bins must be in increasing order");
    fXmin      = fXbins.fArray[0];
    fXmax      = fXbins.fArray[fNbins];
diff --git a/hist/hist/test/test_TH1.cxx b/hist/hist/test/test_TH1.cxx
index 471e8068e4718..73d4ba9f5cef1 100644
--- a/hist/hist/test/test_TH1.cxx
+++ b/hist/hist/test/test_TH1.cxx
@@ -11,6 +11,8 @@
 #include <random>
 #include <vector>
 
+#include "ROOT/TestSupport.hxx"
+
 // StatOverflows TH1
 TEST(TH1, StatOverflows)
 {
@@ -312,3 +314,9 @@ TEST(TH1, SetBufferedSumw2)
    EXPECT_FLOAT_EQ(h1.GetBinContent(1), Entries * Weight);
    EXPECT_FLOAT_EQ(h1.GetBinError(1), std::sqrt(Entries * Weight * Weight));
 }
+
+// https://github.com/root-project/root/issues/20185
+TEST(TAxis, EqualBinEdges)
+{
+   ROOT_EXPECT_ERROR(TAxis _({1, 1}), "TAxis::Set", "bins must be in increasing order");
+}
diff --git a/test/stressHistogram.cxx b/test/stressHistogram.cxx
index 09b3e64750c6a..bfb7361a83806 100644
--- a/test/stressHistogram.cxx
+++ b/test/stressHistogram.cxx
@@ -9185,13 +9185,17 @@ bool testArrayRebin()
       h1->Fill( r.Uniform( minRange * .9 , maxRange * 1.1 ) );
 
    // Create vector - generate bin edges ( nbins is always > 2)
-   // ignore fact that array may contains bins with zero size
    Double_t * rebinArray = new Double_t[rebin];
    r.RndmArray(rebin, rebinArray);
    std::sort(rebinArray, rebinArray + rebin);
    for ( Int_t i = 0; i < rebin; ++i ) {
       rebinArray[i] = TMath::Nint( rebinArray[i] * ( h1->GetNbinsX() - 2 ) + 2 );
       rebinArray[i] = h1->GetBinLowEdge( (Int_t) rebinArray[i] );
+      // compensate for the fact that array may contain bins with zero size
+      if (i > 0) {
+         if (rebinArray[i] <= rebinArray[i - 1])
+            rebinArray[i] = rebinArray[i - 1] + 1e-15;
+      }
    }