diff --git a/Eigen/src/Eigenvalues/ComplexSchur.h b/Eigen/src/Eigenvalues/ComplexSchur.h
index a4812dac6..cf6755bfc 100644
--- a/Eigen/src/Eigenvalues/ComplexSchur.h
+++ b/Eigen/src/Eigenvalues/ComplexSchur.h
@@ -192,6 +192,12 @@ template<typename _MatrixType> class ComplexSchur
       */
     ComplexSchur& compute(const MatrixType& matrix, bool computeU = true);
 
+    /** \brief Maximum number of iterations.
+      *
+      * Maximum number of iterations allowed for an eigenvalue to converge. 
+      */
+    static const int m_maxIterations = 30;
+
   protected:
     ComplexMatrixType m_matT, m_matU;
     HessenbergDecomposition<MatrixType> m_hess;
@@ -374,9 +380,9 @@ void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
     // if iu is zero then we are done; the whole matrix is triangularized
     if(iu==0) break;
 
-    // if we spent 30 iterations on the current element, we give up
+    // if we spent too many iterations on the current element, we give up
     iter++;
-    if(iter >= 30) break;
+    if(iter >= m_maxIterations) break;
 
     // find il, the top row of the active submatrix
     il = iu-1;
@@ -406,7 +412,7 @@ void ComplexSchur<MatrixType>::reduceToTriangularForm(bool computeU)
     }
   }
 
-  if(iter >= 30) 
+  if(iter >= m_maxIterations) 
   {
     // FIXME : what to do when iter==MAXITER ??
     // std::cerr << "MAXITER" << std::endl;
diff --git a/Eigen/src/Eigenvalues/RealSchur.h b/Eigen/src/Eigenvalues/RealSchur.h
index 41f74e530..584b1d05e 100644
--- a/Eigen/src/Eigenvalues/RealSchur.h
+++ b/Eigen/src/Eigenvalues/RealSchur.h
@@ -176,6 +176,12 @@ template<typename _MatrixType> class RealSchur
       */
     RealSchur& compute(const MatrixType& matrix, bool computeU = true);
 
+    /** \brief Maximum number of iterations.
+      *
+      * Maximum number of iterations allowed for an eigenvalue to converge. 
+      */
+    static const int m_maxIterations = 40;
+
   private:
     
     MatrixType m_matT;
@@ -244,14 +250,19 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const MatrixType& matrix,
       Vector3s firstHouseholderVector, shiftInfo;
       computeShift(iu, iter, exshift, shiftInfo);
       iter = iter + 1;   // (Could check iteration count here.)
+      if (iter >= m_maxIterations) break;
       Index im;
       initFrancisQRStep(il, iu, shiftInfo, im, firstHouseholderVector);
       performFrancisQRStep(il, im, iu, computeU, firstHouseholderVector, workspace);
     }
   } 
 
-  m_isInitialized = true;
-  m_matUisUptodate = computeU;
+  if(iter < m_maxIterations) 
+  {
+    m_isInitialized = true;
+    m_matUisUptodate = computeU;
+  }
+
   return *this;
 }
 
diff --git a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
index 20773a549..b08bbd7e2 100644
--- a/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
+++ b/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
@@ -360,6 +360,11 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
       return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
     }
 
+    /** \brief Maximum number of iterations.
+      *
+      * Maximum number of iterations allowed for an eigenvalue to converge. 
+      */
+    static const int m_maxIterations = 30;
 
   protected:
     MatrixType m_eivec;
@@ -419,6 +424,8 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
 
   Index end = n-1;
   Index start = 0;
+  Index iter = 0; // number of iterations we are working on one element
+
   while (end>0)
   {
     for (Index i = start; i<end; ++i)
@@ -427,9 +434,17 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
 
     // find the largest unreduced block
     while (end>0 && m_subdiag[end-1]==0)
+    {
+      iter = 0;
       end--;
+    }
     if (end<=0)
       break;
+
+    // if we spent too many iterations on the current element, we give up
+    iter++;
+    if(iter >= m_maxIterations) break;
+
     start = end - 1;
     while (start>0 && m_subdiag[start-1]!=0)
       start--;
@@ -437,6 +452,11 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
     ei_tridiagonal_qr_step(diag.data(), m_subdiag.data(), start, end, computeEigenvectors ? m_eivec.data() : (Scalar*)0, n);
   }
 
+  if(iter >= m_maxIterations) 
+  {
+    return *this;
+  }
+
   // Sort eigenvalues and corresponding vectors.
   // TODO make the sort optional ?
   // TODO use a better sort algorithm !!