diff --git a/src/CellValues/NonIterableCellMaps.jl b/src/CellValues/NonIterableCellMaps.jl
new file mode 100644
index 000000000..8757788f3
--- /dev/null
+++ b/src/CellValues/NonIterableCellMaps.jl
@@ -0,0 +1,39 @@
+module NonIterableCellMaps
+
+using Gridap
+using Gridap.Helpers
+
+export UnimplementedMap
+export NonIterableCellMap
+import Base: iterate
+import Gridap: evaluate
+import Gridap: return_size
+
+struct UnimplementedMap{S,M,T,N} <: Map{S,M,T,N} end
+
+function evaluate!(
+  this::UnimplementedMap{S,M,T,N},
+  points::AbstractArray{<:S,M},
+  v::AbstractArray{T,N}) where {S,M,T,N}
+  @notimplemented
+end
+
+function return_size(::UnimplementedMap{S,M,T,N},::NTuple{M,Int}) where {S,M,T,N}
+  @notimplemented
+end
+
+abstract type NonIterableCellMap{S,M,T,N} <: IterCellValue{UnimplementedMap{S,M,T,N}} end
+
+function iterate(::NonIterableCellMap)
+  _error()
+end
+
+function iterate(::NonIterableCellMap,state)
+  _error()
+end
+
+function _error()
+  error("Iteration is intentionally disabled for this type.")
+end
+
+end # module
diff --git a/src/CellValues/files.jl b/src/CellValues/files.jl
index 7ccee2bfb..a7f407d64 100644
--- a/src/CellValues/files.jl
+++ b/src/CellValues/files.jl
@@ -50,4 +50,7 @@ include("ConstantCellValues.jl")
 include("CompressedCellValues.jl")
 @reexport using Gridap.CompressedCellValues
 
+include("NonIterableCellMaps.jl")
+@reexport using Gridap.NonIterableCellMaps
+
 
diff --git a/test/CellValuesTests/NonIterableCellMapsTests.jl b/test/CellValuesTests/NonIterableCellMapsTests.jl
new file mode 100644
index 000000000..cd20d75b9
--- /dev/null
+++ b/test/CellValuesTests/NonIterableCellMapsTests.jl
@@ -0,0 +1,22 @@
+module NonIterableCellMapsTests
+
+using Test
+using Gridap
+
+struct Foo <: NonIterableCellMap{Point{2},1,Int,1} end
+
+foo = Foo()
+
+@test isa(foo,CellMap)
+
+try
+  iterate(foo)
+catch LoadError
+end
+
+try
+  iterate(foo,2)
+catch LoadError
+end
+
+end # module
diff --git a/test/CellValuesTests/runtests.jl b/test/CellValuesTests/runtests.jl
index b9891ef6f..33689e678 100644
--- a/test/CellValuesTests/runtests.jl
+++ b/test/CellValuesTests/runtests.jl
@@ -40,5 +40,7 @@ include("MapsMocks.jl")
 
 @testset "CompressedCellValues" begin include("CompressedCellValuesTests.jl") end
 
+@testset "NonIterableCellMaps" begin include("NonIterableCellMapsTests.jl") end
+
 end # module