diff --git a/compiler/kernel/expr.go b/compiler/kernel/expr.go
index 0f5659f8af..aa7c50b03b 100644
--- a/compiler/kernel/expr.go
+++ b/compiler/kernel/expr.go
@@ -315,8 +315,13 @@ func (b *Builder) compileCall(call dag.Call) (expr.Evaluator, error) {
 	var path field.Path
 	// First check if call is to a user defined function, otherwise check for
 	// builtin function.
-	fn, ok := b.funcs[call.Name]
-	if !ok {
+	var fn expr.Function
+	if e, ok := b.udfs[call.Name]; ok {
+		var err error
+		if fn, err = b.compileUDFCall(call.Name, e); err != nil {
+			return nil, err
+		}
+	} else {
 		var err error
 		fn, path, err = function.New(b.zctx(), call.Name, len(call.Args))
 		if err != nil {
@@ -335,6 +340,22 @@ func (b *Builder) compileCall(call dag.Call) (expr.Evaluator, error) {
 	return expr.NewCall(b.zctx(), fn, exprs), nil
 }
 
+func (b *Builder) compileUDFCall(name string, body dag.Expr) (expr.Function, error) {
+	if fn, ok := b.compiledUDFs[name]; ok {
+		return fn, nil
+	}
+	fn := &expr.UDF{}
+	// We store compiled UDF calls here so as to avoid stack overflows on
+	// recursive calls.
+	b.compiledUDFs[name] = fn
+	var err error
+	if fn.Body, err = b.compileExpr(body); err != nil {
+		return nil, err
+	}
+	delete(b.compiledUDFs, name)
+	return fn, nil
+}
+
 func (b *Builder) compileMapCall(a *dag.MapCall) (expr.Evaluator, error) {
 	e, err := b.compileExpr(a.Expr)
 	if err != nil {
diff --git a/compiler/kernel/op.go b/compiler/kernel/op.go
index 018210b503..313f7c3419 100644
--- a/compiler/kernel/op.go
+++ b/compiler/kernel/op.go
@@ -4,6 +4,7 @@ import (
 	"context"
 	"errors"
 	"fmt"
+	"maps"
 	"slices"
 	"strings"
 	"sync"
@@ -50,15 +51,16 @@ import (
 var ErrJoinParents = errors.New("join requires two upstream parallel query paths")
 
 type Builder struct {
-	rctx      *runtime.Context
-	mctx      *zed.Context
-	source    *data.Source
-	readers   []zio.Reader
-	progress  *zbuf.Progress
-	arena     *zed.Arena // For zed.Values created during compilation.
-	deletes   *sync.Map
-	funcs     map[string]expr.Function
-	resetters expr.Resetters
+	rctx         *runtime.Context
+	mctx         *zed.Context
+	source       *data.Source
+	readers      []zio.Reader
+	progress     *zbuf.Progress
+	arena        *zed.Arena // For zed.Values created during compilation.
+	deletes      *sync.Map
+	udfs         map[string]dag.Expr
+	compiledUDFs map[string]*expr.UDF
+	resetters    expr.Resetters
 }
 
 func NewBuilder(rctx *runtime.Context, source *data.Source) *Builder {
@@ -74,8 +76,9 @@ func NewBuilder(rctx *runtime.Context, source *data.Source) *Builder {
 			RecordsRead:    0,
 			RecordsMatched: 0,
 		},
-		arena: arena,
-		funcs: make(map[string]expr.Function),
+		arena:        arena,
+		udfs:         make(map[string]dag.Expr),
+		compiledUDFs: make(map[string]*expr.UDF),
 	}
 }
 
@@ -459,11 +462,14 @@ func (b *Builder) compileSeq(seq dag.Seq, parents []zbuf.Puller) ([]zbuf.Puller,
 }
 
 func (b *Builder) compileScope(scope *dag.Scope, parents []zbuf.Puller) ([]zbuf.Puller, error) {
-	// XXX We need to fix how udfs are compiled since there is currently a bug
-	// where aggregation expressions in udfs do not have separate state per
-	// invocation.
-	if err := b.compileFuncs(scope.Funcs); err != nil {
-		return nil, err
+	// Because there can be name collisions between a child and parent scope
+	// we clone the current udf map, populate the cloned map, then restore the
+	// old scope once the current scope has been built.
+	parentUDFs := b.udfs
+	b.udfs = maps.Clone(parentUDFs)
+	defer func() { b.udfs = parentUDFs }()
+	for _, f := range scope.Funcs {
+		b.udfs[f.Name] = f.Expr
 	}
 	return b.compileSeq(scope.Body, parents)
 }
@@ -510,25 +516,6 @@ func (b *Builder) compileScatter(par *dag.Scatter, parents []zbuf.Puller) ([]zbu
 	return ops, nil
 }
 
-func (b *Builder) compileFuncs(fns []*dag.Func) error {
-	udfs := make([]*expr.UDF, 0, len(fns))
-	for _, f := range fns {
-		if _, ok := b.funcs[f.Name]; ok {
-			return fmt.Errorf("internal error: func %q declared twice", f.Name)
-		}
-		u := &expr.UDF{}
-		b.funcs[f.Name] = u
-		udfs = append(udfs, u)
-	}
-	for i := range fns {
-		var err error
-		if udfs[i].Body, err = b.compileExpr(fns[i].Expr); err != nil {
-			return err
-		}
-	}
-	return nil
-}
-
 func (b *Builder) compileExprSwitch(swtch *dag.Switch, parents []zbuf.Puller) ([]zbuf.Puller, error) {
 	parent := parents[0]
 	if len(parents) > 1 {
diff --git a/runtime/sam/expr/ztests/udf-stateful-expr.yaml b/runtime/sam/expr/ztests/udf-stateful-expr.yaml
new file mode 100644
index 0000000000..b10cdd318b
--- /dev/null
+++ b/runtime/sam/expr/ztests/udf-stateful-expr.yaml
@@ -0,0 +1,9 @@
+zed: |
+  func c1(): ( count() )
+  func c2(): ( c1()+c1() )
+  yield [c2(),c2(),c2()]
+
+input: 'null'
+
+output: |
+  [2(uint64),2(uint64),2(uint64)]