diff --git a/Sources/Container-Compose/Codable Structs/Service.swift b/Sources/Container-Compose/Codable Structs/Service.swift
index 78fcd73..b0950ef 100644
--- a/Sources/Container-Compose/Codable Structs/Service.swift	
+++ b/Sources/Container-Compose/Codable Structs/Service.swift	
@@ -422,6 +422,56 @@ public struct Service: Codable, Hashable {
         return sorted
     }
 
+    /// Groups the selected services into launch WAVES for a parallel `up`. Every
+    /// service in `levels[k]` has all of its in-set `depends_on` dependencies in
+    /// some earlier wave, so every service in one wave can be `container run`
+    /// launched concurrently (issue #128). Level 0 (no in-set dependencies)
+    /// comes first.
+    ///
+    /// - `depends_on` entries naming a service that is not in `services` are
+    ///   ignored — mirroring `topoSortConfiguredServices` and the way
+    ///   profile-excluded dependencies are tolerated.
+    /// - Throws (same `NSError`/"ComposeError" shape as `topoSortConfiguredServices`)
+    ///   on a dependency cycle, including a self-dependency, *before* returning —
+    ///   so a cyclic graph can never deadlock the concurrent launch.
+    /// - Order within a wave follows the caller's service order but is otherwise
+    ///   unspecified (the services in a wave are meant to start concurrently).
+    static func dependencyLevels(
+        _ services: [(serviceName: String, service: Service)]
+    ) throws -> [[String]] {
+        let byName = Dictionary(uniqueKeysWithValues: services.map { ($0.serviceName, $0.service) })
+
+        var level: [String: Int] = [:]
+        var visiting: Set<String> = []
+
+        func computeLevel(_ name: String) throws -> Int {
+            if let cached = level[name] { return cached }
+            guard let service = byName[name] else { return 0 }  // out-of-set dep → already satisfied
+            if visiting.contains(name) {
+                throw NSError(domain: "ComposeError", code: 1, userInfo: [
+                    NSLocalizedDescriptionKey: "Cyclic dependency detected involving '\(name)'"
+                ])
+            }
+            visiting.insert(name)
+            var maxDepLevel = -1
+            for dep in service.depends_on ?? [] where byName[dep] != nil {
+                maxDepLevel = max(maxDepLevel, try computeLevel(dep))
+            }
+            visiting.remove(name)
+            let resolved = maxDepLevel + 1
+            level[name] = resolved
+            return resolved
+        }
+
+        var waves: [[String]] = []
+        for (name, _) in services {
+            let lvl = try computeLevel(name)
+            while waves.count <= lvl { waves.append([]) }
+            waves[lvl].append(name)
+        }
+        return waves
+    }
+
     /// Validates that every explicitly requested service name exists among the
     /// services defined in the compose file. Mirrors `docker compose up <svc>`,
     /// which fails with "no such service: <svc>" rather than silently selecting
diff --git a/Tests/Container-Compose-StaticTests/ParallelSchedulerTests.swift b/Tests/Container-Compose-StaticTests/ParallelSchedulerTests.swift
new file mode 100644
index 0000000..4baf9cd
--- /dev/null
+++ b/Tests/Container-Compose-StaticTests/ParallelSchedulerTests.swift
@@ -0,0 +1,98 @@
+//===----------------------------------------------------------------------===//
+// Copyright © 2025 Morris Richman and the Container-Compose project authors. All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//   https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+//===----------------------------------------------------------------------===//
+
+import Testing
+import Foundation
+@testable import ContainerComposeCore
+
+/// `dependencyLevels` groups services into launch WAVES: every service in
+/// wave k has all of its in-set dependencies in an earlier wave, so a whole
+/// wave can be `container run` launched concurrently. This is the pure,
+/// daemon-free core of the parallel `up` (issue #128).
+@Suite("Parallel Scheduler Levels")
+struct ParallelSchedulerTests {
+
+    @Test("Linear chain is not parallelized: web -> app -> db")
+    func linearChainOrdersByLevel() throws {
+        let web = Service(image: "nginx", depends_on: ["app"])
+        let app = Service(image: "myapp", depends_on: ["db"])
+        let db = Service(image: "postgres", depends_on: nil)
+
+        let levels = try Service.dependencyLevels([("web", web), ("app", app), ("db", db)])
+
+        #expect(levels == [["db"], ["app"], ["web"]])
+    }
+
+    @Test("Independent services form a single wave (the #128 case)")
+    func independentServicesFormOneWave() throws {
+        let a = Service(image: "a", depends_on: nil)
+        let b = Service(image: "b", depends_on: nil)
+        let c = Service(image: "c", depends_on: nil)
+
+        let levels = try Service.dependencyLevels([("a", a), ("b", b), ("c", c)])
+
+        #expect(levels.count == 1)
+        #expect(Set(levels[0]) == ["a", "b", "c"])
+    }
+
+    @Test("Diamond graph groups siblings into the same wave")
+    func diamondGraphGroupsSiblings() throws {
+        // front depends on web+api; web+api both depend on db.
+        let front = Service(image: "front", depends_on: ["web", "api"])
+        let web = Service(image: "web", depends_on: ["db"])
+        let api = Service(image: "api", depends_on: ["db"])
+        let db = Service(image: "db", depends_on: nil)
+
+        let levels = try Service.dependencyLevels(
+            [("front", front), ("web", web), ("api", api), ("db", db)])
+
+        #expect(levels.count == 3)
+        #expect(levels[0] == ["db"])
+        #expect(Set(levels[1]) == ["web", "api"])
+        #expect(levels[2] == ["front"])
+    }
+
+    @Test("A dependency cycle throws instead of deadlocking")
+    func cycleThrows() {
+        let web = Service(image: "web", depends_on: ["app"])
+        let app = Service(image: "app", depends_on: ["web"])
+
+        #expect(throws: (any Error).self) {
+            try Service.dependencyLevels([("web", web), ("app", app)])
+        }
+    }
+
+    @Test("A self-dependency throws")
+    func selfDependencyThrows() {
+        let a = Service(image: "a", depends_on: ["a"])
+
+        #expect(throws: (any Error).self) {
+            try Service.dependencyLevels([("a", a)])
+        }
+    }
+
+    @Test("depends_on naming a service outside the set is ignored")
+    func dependsOnAbsentServiceIsIgnored() throws {
+        // `web` depends on `db`, but `db` is not in the selected set
+        // (e.g. excluded by a profile). It must not hang or throw — `web`
+        // is treated as having no in-set dependency, so it lands in wave 0.
+        let web = Service(image: "nginx", depends_on: ["db"])
+
+        let levels = try Service.dependencyLevels([("web", web)])
+
+        #expect(levels == [["web"]])
+    }
+}