diff --git a/beacon-chain/p2p/discovery.go b/beacon-chain/p2p/discovery.go
index 558363e8e..dda954a63 100644
--- a/beacon-chain/p2p/discovery.go
+++ b/beacon-chain/p2p/discovery.go
@@ -85,6 +85,8 @@ func (s *Service) listenForNewNodes() {
 			log.WithError(err).Error("Could not convert to peer info")
 			continue
 		}
+		// Make sure that peer is not dialed too often, for each connection attempt there's a backoff period.
+		s.Peers().RandomizeBackOff(peerInfo.ID)
 		go func(info *peer.AddrInfo) {
 			if err := s.connectWithPeer(s.ctx, *info); err != nil {
 				log.WithError(err).Tracef("Could not connect with peer %s", info.String())
diff --git a/beacon-chain/p2p/peers/BUILD.bazel b/beacon-chain/p2p/peers/BUILD.bazel
index 447c9924f..cacf31568 100644
--- a/beacon-chain/p2p/peers/BUILD.bazel
+++ b/beacon-chain/p2p/peers/BUILD.bazel
@@ -12,6 +12,7 @@ go_library(
         "//beacon-chain/p2p/peers/scorers:go_default_library",
         "//proto/beacon/p2p/v1:go_default_library",
         "//shared/params:go_default_library",
+        "//shared/rand:go_default_library",
         "//shared/timeutils:go_default_library",
         "@com_github_ethereum_go_ethereum//p2p/enr:go_default_library",
         "@com_github_gogo_protobuf//proto:go_default_library",
diff --git a/beacon-chain/p2p/peers/status.go b/beacon-chain/p2p/peers/status.go
index 48d68f80c..1af875f7d 100644
--- a/beacon-chain/p2p/peers/status.go
+++ b/beacon-chain/p2p/peers/status.go
@@ -24,6 +24,7 @@ package peers
 
 import (
 	"context"
+	"math"
 	"sort"
 	"time"
 
@@ -40,6 +41,7 @@ import (
 	"github.com/prysmaticlabs/prysm/beacon-chain/p2p/peers/scorers"
 	pb "github.com/prysmaticlabs/prysm/proto/beacon/p2p/v1"
 	"github.com/prysmaticlabs/prysm/shared/params"
+	"github.com/prysmaticlabs/prysm/shared/rand"
 	"github.com/prysmaticlabs/prysm/shared/timeutils"
 )
 
@@ -63,6 +65,13 @@ const (
 
 	// InboundRatio is the proportion of our connected peer limit at which we will allow inbound peers.
 	InboundRatio = float64(0.8)
+
+	// MinBackOffDuration minimum amount (in milliseconds) to wait before peer is re-dialed.
+	// When node and peer are dialing each other simultaneously connection may fail. In order, to break
+	// of constant dialing, peer is assigned some backoff period, and only dialed again once that backoff is up.
+	MinBackOffDuration = 100
+	// MaxBackOffDuration maximum amount (in milliseconds) to wait before peer is re-dialed.
+	MaxBackOffDuration = 5000
 )
 
 // Status is the structure holding the peer status information.
@@ -71,6 +80,7 @@ type Status struct {
 	scorers   *scorers.Service
 	store     *peerdata.Store
 	ipTracker map[string]uint64
+	rand      *rand.Rand
 }
 
 // StatusConfig represents peer status service params.
@@ -91,6 +101,9 @@ func NewStatus(ctx context.Context, config *StatusConfig) *Status {
 		store:     store,
 		scorers:   scorers.NewService(ctx, store, config.ScorerParams),
 		ipTracker: map[string]uint64{},
+		// Random generator used to calculate dial backoff period.
+		// It is ok to use deterministic generator, no need for true entropy.
+		rand: rand.NewDeterministicGenerator(),
 	}
 }
 
@@ -336,6 +349,22 @@ func (p *Status) SetNextValidTime(pid peer.ID, nextTime time.Time) {
 	peerData.NextValidTime = nextTime
 }
 
+// RandomizeBackOff adds extra backoff period during which peer will not be dialed.
+func (p *Status) RandomizeBackOff(pid peer.ID) {
+	p.store.Lock()
+	defer p.store.Unlock()
+
+	peerData := p.store.PeerDataGetOrCreate(pid)
+
+	// No need to add backoff period, if the previous one hasn't expired yet.
+	if !time.Now().After(peerData.NextValidTime) {
+		return
+	}
+
+	duration := time.Duration(math.Max(MinBackOffDuration, float64(p.rand.Intn(MaxBackOffDuration)))) * time.Millisecond
+	peerData.NextValidTime = time.Now().Add(duration)
+}
+
 // IsReadyToDial checks where the given peer is ready to be
 // dialed again.
 func (p *Status) IsReadyToDial(pid peer.ID) bool {
diff --git a/endtoend/BUILD.bazel b/endtoend/BUILD.bazel
index 249f8b86e..de7c7b722 100644
--- a/endtoend/BUILD.bazel
+++ b/endtoend/BUILD.bazel
@@ -7,6 +7,7 @@ go_test(
     size = "large",
     testonly = True,
     srcs = [
+        "connectivity_e2e_test.go",
         "endtoend_test.go",
         "minimal_e2e_test.go",
         "minimal_slashing_e2e_test.go",
diff --git a/endtoend/connectivity_e2e_test.go b/endtoend/connectivity_e2e_test.go
new file mode 100644
index 000000000..a39fb226a
--- /dev/null
+++ b/endtoend/connectivity_e2e_test.go
@@ -0,0 +1,31 @@
+package endtoend
+
+import (
+	"testing"
+
+	ev "github.com/prysmaticlabs/prysm/endtoend/evaluators"
+	e2eParams "github.com/prysmaticlabs/prysm/endtoend/params"
+	"github.com/prysmaticlabs/prysm/endtoend/types"
+	"github.com/prysmaticlabs/prysm/shared/params"
+	"github.com/prysmaticlabs/prysm/shared/testutil"
+	"github.com/prysmaticlabs/prysm/shared/testutil/require"
+)
+
+func TestEndToEnd_Connectivity(t *testing.T) {
+	// This test isolates all the preliminary networking setup necessary for other e2e tests.
+	// This allows easier checks for connectivity, discovery and peering issues.
+	testutil.ResetCache()
+	params.UseE2EConfig()
+	require.NoError(t, e2eParams.Init(e2eParams.StandardBeaconCount))
+
+	testConfig := &types.E2EConfig{
+		BeaconFlags:    []string{},
+		ValidatorFlags: []string{},
+		EpochsToRun:    2,
+		Evaluators: []types.Evaluator{
+			ev.PeersConnect,
+		},
+	}
+
+	newTestRunner(t, testConfig).run()
+}