diff --git a/test/solve_ODEs.jl b/test/solve_ODEs.jl
index 00f59a7c6a..a05063637f 100644
--- a/test/solve_ODEs.jl
+++ b/test/solve_ODEs.jl
@@ -110,3 +110,16 @@ for (i,network) in enumerate(reaction_networks_all)
         @test solve(prob,Rosenbrock23()).retcode == :Success
     end
 end
+
+
+### No parameter test ###
+
+no_param_network = @reaction_network begin
+    (1.5,2), ∅ ↔ X
+end
+for factor in [1e0, 1e1, 1e2]
+    u0 = factor*rand(length(no_param_network.states))
+    prob = ODEProblem(no_param_network,u0,(0.,1000.))
+    sol = solve(prob,Rosenbrock23())
+    @test abs.(sol.u[end][1] - 1.5/2) < 1e-8
+end
diff --git a/test/solve_SDEs.jl b/test/solve_SDEs.jl
index a3068b222a..7965ca65dc 100644
--- a/test/solve_SDEs.jl
+++ b/test/solve_SDEs.jl
@@ -138,3 +138,18 @@ for reaction_network in reaction_networks_all
         prob = SDEProblem(reaction_network,u0,(0.,1.),p)
     end
 end
+
+
+### No parameter test ###
+
+no_param_network = @reaction_network begin
+    (1.2,5), X1 ↔ X2
+end
+for factor in [1e3, 1e4]
+    u0 = factor*(1. .+ rand(length(no_param_network.states)))
+    prob = SDEProblem(no_param_network,u0,(0.,1000.))
+    sol = solve(prob,ImplicitEM())
+    vals1 = getindex.(sol.u[1:end],1)
+    vals2 = getindex.(sol.u[1:end],2)
+    @test mean(vals1) > mean(vals2)
+end
diff --git a/test/solve_jumps.jl b/test/solve_jumps.jl
index 8b05c06d4b..8a30c60ee3 100644
--- a/test/solve_jumps.jl
+++ b/test/solve_jumps.jl
@@ -107,3 +107,15 @@ for (i,network) in enumerate(reaction_networks_all)
         @test solve(prob,SSAStepper()).retcode == :Default
     end
 end
+
+no_param_network = @reaction_network begin
+    (1.2,5), X1 ↔ X2
+end
+for factor in [1e1, 1e2]
+    u0 = rand(1:Int64(factor*100),length(no_param_network.states))
+    prob = JumpProblem(no_param_network,DiscreteProblem(no_param_network,u0,(0.,1000.)),Direct())
+    sol = solve(prob,SSAStepper())
+    vals1 = getindex.(sol.u[1:end],1)
+    vals2 = getindex.(sol.u[1:end],2)
+    @test mean(vals1) > mean(vals2)
+end
diff --git a/test/steady_state_problems.jl b/test/steady_state_problems.jl
index 0e49e58cda..e3cd620df4 100644
--- a/test/steady_state_problems.jl
+++ b/test/steady_state_problems.jl
@@ -48,3 +48,15 @@ for network in steady_state_test_networks, factor in [1e-1, 1e0, 1e1]
 
     @test all(abs.(sol_ode.u[end] .- sol_ss.u) .< 1e-4)
 end
+
+
+### No parameter test ###
+
+no_param_network = @reaction_network begin
+    (0.6,3.2), ∅ ↔ X
+end
+for factor in [1e0, 1e1, 1e2]
+    u0 = factor*rand(length(no_param_network.states))
+    sol_ss = solve(SteadyStateProblem(no_param_network,u0),SSRootfind(),abstol=1e-11)
+    @test abs.(sol_ss.u[1]-0.6/3.2) < 1e-8
+end