diff --git a/src/systems/clock_inference.jl b/src/systems/clock_inference.jl
index ee9e92ad03..76c91f61c6 100644
--- a/src/systems/clock_inference.jl
+++ b/src/systems/clock_inference.jl
@@ -285,6 +285,7 @@ function is_time_domain_conversion(v)
     o isa Operator || return false
     itd = input_timedomain(o)
     allequal(itd) || return true
+    isempty(itd) && return true
     otd = output_timedomain(o)
     itd[1] == otd || return true
     return false
diff --git a/src/systems/systemstructure.jl b/src/systems/systemstructure.jl
index b5066a3e98..c867306c34 100644
--- a/src/systems/systemstructure.jl
+++ b/src/systems/systemstructure.jl
@@ -456,7 +456,8 @@ function TearingState(sys; quick_cancel = false, check = true, sort_eqs = true)
 
             if !symbolic_contains(v, dvs)
                 isvalid = iscall(v) &&
-                          (operation(v) isa Shift || is_transparent_operator(operation(v)))
+                          (operation(v) isa Shift || isempty(arguments(v)) ||
+                           is_transparent_operator(operation(v)))
                 v′ = v
                 while !isvalid && iscall(v′) && operation(v′) isa Union{Differential, Shift}
                     v′ = arguments(v′)[1]
diff --git a/src/utils.jl b/src/utils.jl
index 0da7e4860b..355c4858d2 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -633,15 +633,21 @@ can be checked using `check_scope_depth`.
 This function should return `nothing`.
 """
 function collect_vars!(unknowns, parameters, expr, iv; depth = 0, op = Symbolics.Operator)
+    expr = unwrap(expr)
     if issym(expr)
         return collect_var!(unknowns, parameters, expr, iv; depth)
     end
-    for var in vars(expr; op)
-        while iscall(var) && operation(var) isa op
-            validate_operator(operation(var), arguments(var), iv; context = expr)
-            var = arguments(var)[1]
+    varsbuf = OrderedSet()
+    vars!(varsbuf, expr; op)
+    for var in varsbuf
+        if iscall(var) && operation(var) isa op
+            args = arguments(var)
+            validate_operator(operation(var), args, iv; context = expr)
+            isempty(args) && continue
+            push!(varsbuf, args[1])
+        else
+            collect_var!(unknowns, parameters, var, iv; depth)
         end
-        collect_var!(unknowns, parameters, var, iv; depth)
     end
     return nothing
 end
@@ -1184,4 +1190,4 @@ function wrap_with_D(n, D, repeats)
     else
         wrap_with_D(D(n), D, repeats - 1)
     end
-end
\ No newline at end of file
+end
diff --git a/test/clock.jl b/test/clock.jl
index bb16884fe7..6eaed52b73 100644
--- a/test/clock.jl
+++ b/test/clock.jl
@@ -1,6 +1,7 @@
 using ModelingToolkit, Test, Setfield, OrdinaryDiffEq, DiffEqCallbacks
 using ModelingToolkit: ContinuousClock
 using ModelingToolkit: t_nounits as t, D_nounits as D
+using Symbolics, SymbolicUtils
 
 function infer_clocks(sys)
     ts = TearingState(sys)
@@ -146,6 +147,29 @@ eqs = [yd ~ Sample(dt)(y)
     @test varmap[z] == clk
 end
 
+struct ZeroArgOp <: Symbolics.Operator end
+(o::ZeroArgOp)() = Symbolics.Term{Bool}(o, Any[])
+SymbolicUtils.promote_symtype(::ZeroArgOp, T) = Union{Bool, T}
+SymbolicUtils.isbinop(::ZeroArgOp) = false
+Base.nameof(::ZeroArgOp) = :ZeroArgOp
+ModelingToolkit.input_timedomain(::ZeroArgOp, _ = nothing) = ()
+ModelingToolkit.output_timedomain(::ZeroArgOp, _ = nothing) = Clock(0.1)
+ModelingToolkit.validate_operator(::ZeroArgOp, args, iv; context = nothing) = nothing
+SciMLBase.is_discrete_time_domain(::ZeroArgOp) = true
+
+@testset "Zero-argument clock operators" begin
+    @variables x(t) y(t)
+    clk = Clock(0.1)
+    eqs = [D(x) ~ x
+           y ~ ZeroArgOp()()]
+    @named sys = System(eqs, t)
+    @test issetequal(unknowns(sys), [x, y])
+    ts = TearingState(sys)
+    @test issetequal(ts.fullvars, [D(x), x, y, ZeroArgOp()()])
+    ci, clkmap = infer_clocks(sys)
+    @test clkmap[ZeroArgOp()()] == clk
+end
+
 @test_skip begin
     Tf = 1.0
     prob = ODEProblem(