diff --git a/src/ModelingToolkit.jl b/src/ModelingToolkit.jl
index 5ad35ad2ce..cc4f3e8d4a 100644
--- a/src/ModelingToolkit.jl
+++ b/src/ModelingToolkit.jl
@@ -30,6 +30,7 @@ include("differentials.jl")
 include("equations.jl")
 include("systems/diffeqs/diffeqsystem.jl")
 include("systems/diffeqs/first_order_transform.jl")
+include("systems/diffeqs/pantelides.jl")
 include("systems/nonlinear/nonlinear_system.jl")
 include("function_registration.jl")
 include("simplify.jl")
diff --git a/src/systems/diffeqs/pantelides.jl b/src/systems/diffeqs/pantelides.jl
new file mode 100644
index 0000000000..49a0561c86
--- /dev/null
+++ b/src/systems/diffeqs/pantelides.jl
@@ -0,0 +1,76 @@
+struct BiGraph{TA,TB,TC}
+    eqs::TA
+    vars::TB
+    edges::TC
+end
+
+function init_assign(G)
+    assign = Dict{eltype(G.vars), Union{Nothing, eltype(G.eqs)}}()
+    # second function
+    for j in G.vars
+        assign[j] = nothing
+    end
+    return assign
+end
+
+function augmentpath!(i, pathfound, color, assign, vars, edges)
+    union!(color, i)
+    idx = -1
+    for j in vars
+        assign[j] === nothing || continue
+        (i => j) in edges && (idx = j; break)
+    end
+    if idx != -1
+        pathfound[] = true
+        assign[idx] = i
+        return nothing
+    end
+    for j in vars
+        !((i => j) in edges && !(j in color)) && continue
+        union!(color, j)
+        k = assign[j]
+        augmentpath!(k, pathfound, color, assign, vars, edges)
+        pathfound[] && (assign[j] = i; return nothing)
+    end
+    return nothing
+end
+
+function construct_augmentpath!(G, assign, pathfound)
+    #main operation in function
+    color = Set(similar(G.eqs, 0))
+    for i in G.eqs
+        empty!(color)
+        pathfound[] = false
+        while !pathfound[]
+            pathfound[] = false
+            augmentpath!(i, pathfound, color, assign, G.vars, G.edges)
+            pathfound[] || break
+        end
+    end
+    return nothing
+end
+
+#function pantelides(m,n,G,diff)
+#    assign = Dict()
+#    b = Dict()
+#    for j=1:m  # dict and vector() which is better. for loop?
+#        assign[j] = 0
+#    end
+#    for j=1:n
+#        b[j] = 0
+#    end
+#    pathfound = false
+#    for k = 1:n
+#        while !pathfound
+#            # 3b-1
+#            filter!(a -> a!=0,diff)
+#            filter!(a -> a[2] in diff,G.edges)
+#            color=Vector()
+#            pathfound=Ref(false)
+#            augmentpath!(k,pathfound,color,assign,G.vars,G.edges)
+#            # 3b-5 to do
+#            pathfound[] || return assign
+#        end
+#    end
+#    return assign
+#end
diff --git a/test/pantelides.jl b/test/pantelides.jl
new file mode 100644
index 0000000000..b28a6aaa52
--- /dev/null
+++ b/test/pantelides.jl
@@ -0,0 +1,36 @@
+using Test
+using ModelingToolkit: BiGraph, construct_augmentpath!, init_assign
+
+function augment_path(G)
+  assign = init_assign(G)
+  pathfound = Ref(false)
+  construct_augmentpath!(G, assign, pathfound)
+  return assign, pathfound[]
+end
+
+# E node using integer from 1 represents the equation mark (the first
+# Vector in BiGraph). V node using integer from 11 represents the variables
+# (the second vector) Edge in the third part represents their relations
+
+G = BiGraph([1, 2, 3, 4, 5], [11, 12, 13, 14, 15, 16, 17, 18, 19], [1=>15, 2=>16, 3=>17, 4=>18, 3=>19, 4=>19, 5=>0])
+#test1 pantelides fig1-b trivial test
+@test augment_path(G) == (Dict(11=>nothing,12=>nothing,13=>nothing,14=>nothing,15=>1,16=>2,17=>3,18=>4,19=>nothing), false)
+
+G = BiGraph([1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [1=>15, 2=>16, 3=>17, 4=>18, 3=>19, 4=>19, 5=>0, 6=>15, 6=>16, 7=>20, 8=>21])
+@test augment_path(G) == (Dict(11=>nothing,12=>nothing,13=>nothing,14=>nothing,15=>1,16=>2,17=>3,18=>4,19=>nothing,20=>7,21=>8), false)
+
+G = BiGraph([1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [1=>15, 2=>16, 3=>17, 4=>18, 3=>19, 4=>19, 5=>0, 7=>20, 8=>21, 7=>17, 8=>18, 9=>20, 9=>21])
+#test3 pantelides fig1-d test
+@test augment_path(G) == (Dict(11=>nothing,12=>nothing,13=>nothing,14=>nothing,15=>1,16=>2,17=>7,18=>4,19=>3,20=>9,21=>8), true)
+
+G = BiGraph([1, 2, 3, 4], [11, 12, 13, 14, 15, 16], [1=>13, 1=>15, 2=>14, 2=>15, 2=>16, 3=>15])
+#test4 pantelides fig2-b test
+@test augment_path(G) == (Dict(11=>nothing,12=>nothing,13=>1,14=>2,15=>3,16=>nothing), false)
+
+G = BiGraph([1, 2, 3, 4, 5, 6, 7, 8], [11, 12, 13, 14, 15, 16, 17, 18], [1=>13, 2=>14, 2=>16, 3=>15, 4=>0, 5=>0, 6=>17, 6=>18, 7=>14, 7=>18, 8=>17])
+#test5 pantelides fig2-d test
+@test augment_path(G) == (Dict(11=>nothing,12=>nothing,13=>1,14=>7,15=>3,16=>2,17=>8,18=>6), true)
+
+G = BiGraph([1, 2, 3, 4], [11, 12, 13, 14], [1=>13, 1=>14, 2=>12, 1=>0])
+#test6 pantelides fig3-b trivial test
+@test augment_path(G) == (Dict(11=>nothing,12=>2,13=>1,14=>nothing), false)
diff --git a/test/runtests.jl b/test/runtests.jl
index 00a80ece02..bc13b49024 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -4,3 +4,4 @@ using ModelingToolkit, Test
 @testset "Differentiation Test" begin include("derivatives.jl") end
 @testset "Simplify Test" begin include("simplify.jl") end
 @testset "System Construction Test" begin include("system_construction.jl") end
+@testset "Pantelides Test" begin include("pantelides.jl") end